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arxiv: 2607.00618 · v1 · pith:NDNXZ3A6new · submitted 2026-07-01 · ⚛️ physics.optics

Generation of strongly localized skin solitons in non-Hermitian waveguide arrays with the Kerr effect

Chong Hou , Boris A. Malomed , Qin Zhou This is my paper

Pith reviewed 2026-07-02 07:26 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords non-Hermitian skin effectKerr nonlinearitywaveguide arraysskin solitonssymbolic regressionsoliton existence boundarynon-reciprocal couplingsedge localization
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The pith

Kerr nonlinearity and the non-Hermitian skin effect together generate stable skin solitons localized at the edge of waveguide arrays.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines light propagation in non-reciprocal waveguide arrays under the Kerr nonlinearity. Single-channel excitation produces stable solitons through the combined action of nonlinearity and the non-Hermitian skin effect. Symbolic regression supplies a closed-form expression for the boundary of soliton existence. Broad initial pulses evolve into perturbed solitons whose propagation is accelerated by the skin effect, resulting in strong edge localization. Stationary solutions include nonlinear bulk modes that are driven toward the edge when non-reciprocality is present, constituting a nonlinear version of the skin effect.

Core claim

Single-channel excitation creates stable solitons supported by the interplay of the Kerr nonlinearity and non-Hermitian skin effect. An analytical formula defining the soliton existence boundary is obtained by the symbolic-regression method. For broad-pulse excitation, perturbed soliton solutions are derived in the continuum approximation and show that the skin effect accelerates propagation toward the boundary, ultimately causing tight localization at the edge. Stationary nonlinear bulk modes in the Hermitian regime become compressed toward the edge under non-reciprocality, which is identified as the nonlinear extension of the non-Hermitian skin effect.

What carries the argument

The non-Hermitian skin effect in interplay with Kerr nonlinearity, which supports stable localized solitons and supplies the mechanism for edge compression of bulk modes.

If this is right

  • Single-channel initial conditions reliably produce stable solitons localized by the skin effect.
  • The existence region of these solitons is delimited by an explicit analytical formula obtained from symbolic regression.
  • Broad pulses experience accelerated motion to the array edge and form tightly localized states.
  • Nonlinear bulk modes are compressed toward the edge once non-reciprocal couplings are introduced.
  • Near-edge skin solitons appear as stationary solutions in the non-Hermitian regime.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The derived boundary formula could be used to predict the minimal nonlinearity strength needed for edge localization in similar discrete non-Hermitian lattices.
  • The observed acceleration of broad pulses suggests that non-Hermitian couplings might serve as a passive mechanism for routing optical power to boundaries without external modulation.
  • The nonlinear skin-effect compression of bulk modes may extend to other conservative nonlinearities, offering a route to edge-mode engineering in photonic arrays.
  • Testing the same initial conditions in a continuum non-Hermitian nonlinear Schrödinger equation would check whether the localization persists without lattice discreteness.

Load-bearing premise

The symbolic-regression procedure produces a physically valid closed-form expression for the existence boundary rather than an overfit artifact, and the continuum approximation remains accurate for the broad-pulse dynamics in the discrete lattice.

What would settle it

Direct numerical integration of the discrete lattice equations that either confirms or refutes the persistence of stable solitons for parameter values lying just inside versus just outside the analytically predicted existence boundary.

Figures

Figures reproduced from arXiv: 2607.00618 by Boris A. Malomed, Chong Hou, Qin Zhou.

Figure 1
Figure 1. Figure 1: FIG. 1. The schematic of the nonreciprocal nonlinear non-Hermitian [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Solitons in WGAs (with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The existence threshold for the lattice solitons in the nonlinear [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: compares the dynamical behavior produced by the numerical simulations of the continuum approximation, Eq. (12), and the underlying discrete HN model (1) for broad￾envelope initial excitation. For this purpose, Eq. (12) was solved with input 𝑢0 = 𝜂0sech(𝜂0𝑥)𝑒 𝑖𝑐𝑥, while the initial con￾dition for the discrete equation (1) was taken as 𝑈 = 𝑢 ∗ 0 / √︁ |𝜎|, with 𝑥 = 𝑛/ √ 2𝐶. The simulations reveal that the pul… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Dynamical simulations of light propagation from [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Hermitian nonlinear propagation constant [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The nonlinear HN skin solitons and their energy spectrum. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The comparison of the final energy spectra and selected [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

We address two distinct nonlinear propagation problems in nonlinear optical waveguide arrays (WGAs) with non-reciprocal (non-Hermitian) couplings. First, we investigate the light propagation launched by initial excitations of two different types. The single-channel excitation creates stable solitons supported by the interplay of the Kerr nonlinearity and non-Hermitian skin effect (NHSE). In this case, we derive, by means of the symbolic-regression method, an analytical formula defining the soliton existence boundary. For the broad-pulse excitation, we produce perturbed soliton solutions analytically in the continuum approximation, which is accurately corroborated by numerical results. We thus conclude that NHSE accelerates the propagation of the broad soliton towards the boundary, ultimately causing tight localization at the edge, which is a hallmark of the NHSE in the continuum limit. Second, we identify stationary solitons in the system -- specifically, nonlinear bulk modes in the Hermitian regime and near-edge skin solitons in the non-Hermitian one. The nonlinear bulk modes are compressed toward the edge of the WGA under the action of the non-reciprocality, which is the nonlinear extension of NHSE.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript studies nonlinear light propagation in non-Hermitian waveguide arrays with Kerr nonlinearity. Single-channel excitation is shown to produce stable solitons via the interplay of Kerr nonlinearity and the non-Hermitian skin effect (NHSE); an analytical expression for the soliton existence boundary is obtained by symbolic regression. For broad-pulse initial conditions, perturbed soliton solutions are derived in the continuum approximation and stated to be corroborated by numerics, with NHSE driving edge localization. Stationary solutions are also identified: nonlinear bulk modes in the Hermitian limit that become compressed toward the edge under non-reciprocality, and near-edge skin solitons in the non-Hermitian regime.

Significance. If the symbolic-regression formula proves robust and the numerical validations hold, the work supplies concrete analytical and numerical results on nonlinear extensions of the NHSE in both discrete and continuum settings. The explicit formula for the existence boundary and the demonstration of NHSE-driven localization constitute potentially useful benchmarks for experiments in non-Hermitian nonlinear optics.

major comments (2)
  1. [single-channel excitation / symbolic regression section] The central analytical result—the closed-form expression for the soliton existence boundary—is obtained exclusively via symbolic regression. No information is provided on the regression search space, regularization, cross-validation procedure, or quantitative error metrics evaluated on independent parameter points outside the training set. Without these, it is impossible to determine whether the formula is a physically interpretable relation or an overfit artifact whose agreement with the reported trajectories is circular (§ on single-channel excitation and symbolic regression).
  2. [broad-pulse excitation / continuum approximation] The claim that the continuum approximation remains accurate for broad-pulse dynamics rests on numerical corroboration, yet the manuscript does not report quantitative measures (e.g., L2 error between continuum solution and discrete lattice evolution, or dependence on lattice spacing) that would confirm the approximation's validity across the parameter range used for the existence boundary.
minor comments (2)
  1. Notation for the non-reciprocal coupling parameters and the Kerr coefficient should be introduced once with explicit definitions before being used in multiple sections.
  2. Figure captions for the soliton profiles should state the precise values of the non-Hermitian parameter and nonlinearity strength used in each panel.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and quantitative validations.

read point-by-point responses

  1. Referee: [single-channel excitation / symbolic regression section] The central analytical result—the closed-form expression for the soliton existence boundary—is obtained exclusively via symbolic regression. No information is provided on the regression search space, regularization, cross-validation procedure, or quantitative error metrics evaluated on independent parameter points outside the training set. Without these, it is impossible to determine whether the formula is a physically interpretable relation or an overfit artifact whose agreement with the reported trajectories is circular (§ on single-channel excitation and symbolic regression).

    Authors: We agree that additional methodological details are required to establish the robustness of the symbolic-regression result. In the revised manuscript we will expand the relevant section to specify the search space of operators and functions, any regularization employed, the cross-validation protocol, and quantitative error metrics (e.g., RMSE) evaluated on an independent test set of parameter points. These additions will demonstrate that the formula is not an overfitting artifact and that the numerical trajectories used for comparison were generated independently of the regression training data. revision: yes

  2. Referee: [broad-pulse excitation / continuum approximation] The claim that the continuum approximation remains accurate for broad-pulse dynamics rests on numerical corroboration, yet the manuscript does not report quantitative measures (e.g., L2 error between continuum solution and discrete lattice evolution, or dependence on lattice spacing) that would confirm the approximation's validity across the parameter range used for the existence boundary.

    Authors: We concur that quantitative error measures are necessary to substantiate the continuum approximation. In the revision we will add explicit L2-error comparisons between the continuum solutions and discrete-lattice simulations, together with the dependence of this error on lattice spacing, evaluated across the parameter regime of the existence boundary. These metrics will replace the current visual corroboration and confirm the approximation's accuracy. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivations are self-contained

full rationale

The paper's central results—an analytical formula for the soliton existence boundary obtained via symbolic regression and perturbed soliton solutions in the continuum limit—are derived from numerical simulations and analytical approximations respectively, with explicit numerical corroboration stated for the latter. No quoted equations or steps reduce by construction to their own inputs, fitted parameters renamed as predictions, or load-bearing self-citations. The symbolic-regression step is a data-driven fitting procedure presented as yielding a closed-form expression, but without evidence in the text of it being tautological or statistically forced on the same trajectories used for validation. The overall derivation chain therefore remains independent of the target claims.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the work rests on standard discrete nonlinear Schrödinger models augmented by non-reciprocal coupling terms whose precise form is not given here.

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Reference graph

Works this paper leans on

77 extracted references · 3 canonical work pages · 1 internal anchor

  1. [1]

    Coupling of optical fibers and scattering in fibers*,

    A. L. Jones, “Coupling of optical fibers and scattering in fibers*,” J. Opt. Soc. Am.55, 261 (1965)

    1965

  2. [2]

    Discrete spatial optical solitons in waveguide ar- rays,

    H. Eisenberg, Y. Silberberg, R. Morandotti, A. Boyd, and J. Aitchison, “Discrete spatial optical solitons in waveguide ar- rays,” Phys. Rev. Lett.81, 3383 (1998)

    1998

  3. [3]

    P. G. Kevrekidis and R. Carretero-Gonz ´alez,The discrete non- linear schr¨odinger equation: Mathematical analysis, numerical computations and physical perspectives, Springer tracts in mod- ern physics No. 232 (Springer, Berlin [London], 2009)

    2009

  4. [4]

    Discrete optics in femtosecond-laser- written photonic structures,

    A. Szameit and S. Nolte, “Discrete optics in femtosecond-laser- written photonic structures,” J. Phys. B43, 163001 (2010)

    2010

  5. [5]

    Topological gap solitons in equidistant Lithium Niobate waveguide arrays,

    A. V. Gorbach, “Topological gap solitons in equidistant Lithium Niobate waveguide arrays,” Low Temp. Phys.51, 737 (2025)

    2025

  6. [6]

    Non-Bloch band theory of non-Hermitian systems,

    K. Yokomizo and S. Murakami, “Non-Bloch band theory of non-Hermitian systems,” Phys. Rev. Lett.123, 066404 (2019). 9

    2019

  7. [7]

    Topological photonics,

    T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, “Topological photonics,” Rev. Mod. Phys.91, 015006 (2019)

    2019

  8. [8]

    Roadmap on topological photonics,

    H. Price, Y. Chong, A. Khanikaev, H. Schomerus, L. J. Maczewsky, M. Kremer, M. Heinrich, A. Szameit, O. Zilber- berg, Y. Yang, B. Zhang, A. Al` u, R. Thomale, I. Carusotto, P. St-Jean, A. Amo, A. Dutt, L. Yuan, S. Fan, X. Yin, C. Peng, T. Ozawa, and A. Blanco-Redondo, “Roadmap on topological photonics,” J. Phys. Photonics4, 032501 (2022)

    2022

  9. [9]

    Advances and applications on non-Hermitian topological photonics,

    Q. Yan, B. Zhao, R. Zhou, R. Ma, Q. Lyu, S. Chu, X. Hu, and Q. Gong, “Advances and applications on non-Hermitian topological photonics,” Nanophotonics12, 2247 (2023)

    2023

  10. [10]

    Artificial gauge fields in photonics,

    W. Song, Y. Yang, Z. Lin, X. Liu, S. Wu, C. Chen, Y. Ke, C. Lee, W. Liu, S. Zhu, Y. Kivshar, T. Li, and S. Zhang, “Artificial gauge fields in photonics,” Nat Rev Phys7, 606 (2025)

    2025

  11. [11]

    A review on non-Hermitian skin effect,

    X. Zhang, T. Zhang, M.-H. Lu, and Y.-F. Chen, “A review on non-Hermitian skin effect,” Adv. Phys.: X7, 2109431 (2022)

    2022

  12. [12]

    Topo- logical funneling of light,

    S. Weidemann, M. Kremer, T. Helbig, T. Hofmann, A. Stegmaier, M. Greiter, R. Thomale, and A. Szameit, “Topo- logical funneling of light,” Science368, 311 (2020)

    2020

  13. [13]

    Mobility transition from ballistic to diffusive transport in non-Hermitian lattices,

    T. Eichelkraut, R. Heilmann, S. Weimann, S. St¨ utzer, F. Dreisow, D. N. Christodoulides, S. Nolte, and A. Szameit, “Mobility transition from ballistic to diffusive transport in non-Hermitian lattices,” Nat. Commun.4, 2533 (2013)

    2013

  14. [14]

    Non-Hermitian tight-binding network engineering,

    S. Longhi, “Non-Hermitian tight-binding network engineering,” Phys. Rev. A93, 022102 (2016)

    2016

  15. [15]

    Topologi- cal framework for directional amplification in driven-dissipative cavity arrays,

    C. C. Wanjura, M. Brunelli, and A. Nunnenkamp, “Topologi- cal framework for directional amplification in driven-dissipative cavity arrays,” Nat. Commun.11, 3149 (2020)

    2020

  16. [16]

    Controlling light transport in non-Hermitian waveguide arrays,

    C. Hou, H. Triki, and Q. Zhou, “Controlling light transport in non-Hermitian waveguide arrays,” Opt. Express33, 40423 (2025)

    2025

  17. [17]

    Spawning rings of exceptional points out of Dirac cones,

    B. Zhen, C. W. Hsu, Y. Igarashi, L. Lu, I. Kaminer, A. Pick, S.-L. Chua, J. D. Joannopoulos, and M. Solja ˇci´c, “Spawning rings of exceptional points out of Dirac cones,” Nature525, 354 (2015)

    2015

  18. [18]

    Experimental realization of a Weyl exceptional ring,

    A. Cerjan, S. Huang, M. Wang, K. P. Chen, Y. Chong, and M. C. Rechtsman, “Experimental realization of a Weyl exceptional ring,” Nat. Photon.13, 623 (2019)

    2019

  19. [19]

    Exceptional points in optics and pho- tonics,

    M.-A. Miri and A. Al` u, “Exceptional points in optics and pho- tonics,” Science363, eaar7709 (2019)

    2019

  20. [20]

    Photonic Floquet topological insulators,

    M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podol- sky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, “Photonic Floquet topological insulators,” Nature496, 196 (2013)

    2013

  21. [21]

    Nonlinear tuning of PT sym- metry and non-Hermitian topological states,

    S. Xia, D. Kaltsas, D. Song, I. Komis, J. Xu, A. Szameit, H. Bul- jan, K. G. Makris, and Z. Chen, “Nonlinear tuning of PT sym- metry and non-Hermitian topological states,” Science372, 72 (2021)

    2021

  22. [22]

    Eigenvalue control and switching by fission of multisoliton bound states in planar waveguides,

    V. A. Aleshkevich, Y. V. Kartashov, A. S. Zelenina, V. A. Vysloukh, J. P. Torres, and L. Torner, “Eigenvalue control and switching by fission of multisoliton bound states in planar waveguides,” Opt. Lett.29, 483 (2004)

    2004

  23. [23]

    Spa- tiotemporal optical solitons,

    B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spa- tiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt.7, R53 (2005)

    2005

  24. [24]

    Surface gap solitons,

    Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett.96, 073901 (2006)

    2006

  25. [25]

    Gap solitons on a ring,

    Y. V. Kartashov, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Gap solitons on a ring,” Opt. Lett.33, 2949 (2008)

    2008

  26. [26]

    Solitons in nonlinear lattices,

    Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys.83, 247 (2011)

    2011

  27. [27]

    Multidimensional solitons: well-established results and novel findings,

    B. A. Malomed, “Multidimensional solitons: well-established results and novel findings,” Eur. Phys. J. Spec. Top.225, 2507 (2016)

    2016

  28. [28]

    Frontiers in multidimensional self-trapping of non- linear fields and matter,

    Y. V. Kartashov, G. E. Astrakharchik, B. A. Malomed, and L. Torner, “Frontiers in multidimensional self-trapping of non- linear fields and matter,” Nat Rev Phys1, 185 (2019)

    2019

  29. [29]

    Nonlinear topological photonics,

    D. Smirnova, D. Leykam, Y. Chong, and Y. Kivshar, “Nonlinear topological photonics,” Appl. Phys. Rev.7, 021306 (2020)

    2020

  30. [30]

    Non-Hermitian and topological pho- tonics: optics at an exceptional point,

    M. Parto, Y. G. N. Liu, B. Bahari, M. Khajavikhan, and D. N. Christodoulides, “Non-Hermitian and topological pho- tonics: optics at an exceptional point,” Nanophotonics10, 403 (2020)

    2020

  31. [31]

    A second wave of topological phenomena in photonics and acoustics,

    X. Zhang, F. Zangeneh-Nejad, Z.-G. Chen, M.-H. Lu, and J. Christensen, “A second wave of topological phenomena in photonics and acoustics,” Nature618, 687 (2023)

    2023

  32. [32]

    Nonlinearity-induced transition in the nonlinear Su-Schrieffer-Heeger model and a nonlinear higher-order topo- logical system,

    M. Ezawa, “Nonlinearity-induced transition in the nonlinear Su-Schrieffer-Heeger model and a nonlinear higher-order topo- logical system,” Phys. Rev. B104, 235420 (2021)

    2021

  33. [33]

    Skin solitons,

    I. Komis, Z. H. Musslimani, and K. G. Makris, “Skin solitons,” Opt. Lett.48, 6525 (2023)

    2023

  34. [34]

    Quantized nonlinear Thouless pumping,

    M. J¨ urgensen, S. Mukherjee, and M. C. Rechtsman, “Quantized nonlinear Thouless pumping,” Nature596, 63 (2021)

    2021

  35. [35]

    Quantization and its breakdown in a Hubbard–Thouless pump,

    A.-S. Walter, Z. Zhu, M. G ¨achter, J. Minguzzi, S. Roschinski, K. Sandholzer, K. Viebahn, and T. Esslinger, “Quantization and its breakdown in a Hubbard–Thouless pump,” Nat. Phys. 19, 1471 (2023)

    2023

  36. [36]

    Self- induced topological protection in nonlinear circuit arrays,

    Y. Hadad, J. C. Soric, A. B. Khanikaev, and A. Al` u, “Self- induced topological protection in nonlinear circuit arrays,” Nat Electron1, 178 (2018)

    2018

  37. [37]

    Observation of Floquet solitons in a topological bandgap,

    S. Mukherjee and M. C. Rechtsman, “Observation of Floquet solitons in a topological bandgap,” Science368, 856 (2020)

    2020

  38. [38]

    Topological solitons in arrays of modelocked lasers,

    A. Y. Zykin, D. V. Skryabin, and Y. V. Kartashov, “Topological solitons in arrays of modelocked lasers,” Opt. Lett.46, 2123 (2021)

    2021

  39. [39]

    Theory of topological corner state laser in Kagome waveguide arrays,

    H. Zhong, Y. V. Kartashov, A. Szameit, Y. Li, C. Liu, and Y. Zhang, “Theory of topological corner state laser in Kagome waveguide arrays,” APL Photonics6(2021)

    2021

  40. [40]

    Topological temporally mode-locked laser,

    C. R. Leefmans, M. Parto, J. Williams, G. H. Y. Li, A. Dutt, F. Nori, and A. Marandi, “Topological temporally mode-locked laser,” Nat. Phys.20, 852 (2024)

    2024

  41. [41]

    Edge states and topological invariants of non-Hermitian systems,

    S. Yao and Z. Wang, “Edge states and topological invariants of non-Hermitian systems,” Phys. Rev. Lett.121, 086803 (2018)

    2018

  42. [42]

    Non-Hermitian skin effect and chiral damping in open quantum systems,

    F. Song, S. Yao, and Z. Wang, “Non-Hermitian skin effect and chiral damping in open quantum systems,” Phys. Rev. Lett.123, 170401 (2019)

    2019

  43. [43]

    Universal non-Hermitian skin effect in two and higher dimensions,

    K. Zhang, Z. Yang, and C. Fang, “Universal non-Hermitian skin effect in two and higher dimensions,” Nat. Commun.13, 2496 (2022)

    2022

  44. [44]

    The non- Hermitian skin effect: A perspective,

    J. T. Gohsrich, A. Banerjee, and F. K. Kunst, “The non- Hermitian skin effect: A perspective,” EPL150, 60001 (2025)

    2025

  45. [45]

    Deterministic bulk-boundary correspondences for skin and edge modes in a general two-band non-Hermitian system,

    C. Hou, L. Li, S. Chen, Y. Liu, L. Yuan, Y. Zhang, and Z. Ni, “Deterministic bulk-boundary correspondences for skin and edge modes in a general two-band non-Hermitian system,” Phys. Rev. Research4, 043222 (2022)

    2022

  46. [46]

    Topological edge states in one-dimensional non-Hermitian Su- Schrieffer-Heeger systems of finite lattice size: analytical solu- tions and exceptional points,

    C. Hou, L. Li, G. Wu, Y. Ruan, S. Chen, and F. Baronio, “Topological edge states in one-dimensional non-Hermitian Su- Schrieffer-Heeger systems of finite lattice size: analytical solu- tions and exceptional points,” Phys. Rev. B108, 085425 (2023)

    2023

  47. [47]

    Non-Hermitian skin effects in two- and three- dimensional intertwined tight-binding lattices,

    C. Hou, G. Wu, L. Li, A. Basit, Y. Wei, S. Chen, P. Grelu, and Z. Ni, “Non-Hermitian skin effects in two- and three- dimensional intertwined tight-binding lattices,” Phys. Rev. B 109, 205135 (2024)

    2024

  48. [48]

    Dual bulk-boundary correspondence in a nonreciprocal spin- orbit coupled zigzag lattice,

    L. Li, C. Hou, G. Wu, Y. Ruan, S. Chen, L. Yuan, and Z. Ni, “Dual bulk-boundary correspondence in a nonreciprocal spin- orbit coupled zigzag lattice,” Phys. Rev. B110, L041103 (2024)

    2024

  49. [49]

    Exact solutions disentangle higher-order topology in two-dimensional non-Hermitian lattices,

    L. Li, Y. Wei, G. Wu, Y. Ruan, S. Chen, C. H. Lee, and 10 Z. Ni, “Exact solutions disentangle higher-order topology in two-dimensional non-Hermitian lattices,” Phys. Rev. B111, 075132 (2025)

    2025

  50. [50]

    Non-Hermitian topological lattice photonics: an analytic per- spective,

    S. Chen, A. Basit, L. Li, C. Hou, Y. Ruan, Y. Wei, and Z. Ni, “Non-Hermitian topological lattice photonics: an analytic per- spective,” Adv. Photonics Res.6, 2500083 (2025)

    2025

  51. [51]

    Observation of flat-band skin effect

    X. Wang, D. Wang, C. Lu, R.-Y. Zhang, C. H. Lee, K. Ding, and G. Ma, “Observation of flat-band skin effect,” arXiv (2025), 10.48550/arXiv.2512.19745

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2512.19745 2025

  52. [52]

    Nonlinear non-Hermitian skin effect and skin soli- tons in temporal photonic feedforward lattices,

    S. Wang, B. Wang, C. Liu, C. Qin, L. Zhao, W. Liu, S. Longhi, and P. Lu, “Nonlinear non-Hermitian skin effect and skin soli- tons in temporal photonic feedforward lattices,” Phys. Rev. Lett. 134(2025)

    2025

  53. [53]

    Skin modes in a nonlinear Hatano-Nelson model,

    B. Many Manda, R. Carretero-Gonz ´alez, P. G. Kevrekidis, and V. Achilleos, “Skin modes in a nonlinear Hatano-Nelson model,” Phys. Rev. B109, 094308 (2024)

    2024

  54. [54]

    Localization transitions in non- Hermitian quantum mechanics,

    N. Hatano and D. R. Nelson, “Localization transitions in non- Hermitian quantum mechanics,” Phys. Rev. Lett.77, 570 (1996)

    1996

  55. [55]

    Complex skin modes in non-Hermitian coupled laser arrays,

    Y. G. N. Liu, Y. Wei, O. Hemmatyar, G. G. Pyrialakos, P. S. Jung, D. N. Christodoulides, and M. Khajavikhan, “Complex skin modes in non-Hermitian coupled laser arrays,” Light Sci Appl11, 336 (2022)

    2022

  56. [56]

    Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of the skin effect,

    C.-X. Guo, C.-H. Liu, X.-M. Zhao, Y. Liu, and S. Chen, “Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of the skin effect,” Phys. Rev. Lett.127, 116801 (2021)

    2021

  57. [57]

    Quantum walk classical simulation with slot waveguide array for sensing,

    Q. Ma, Y. Wang, F. Qi, Z. Liu, and W. Zheng, “Quantum walk classical simulation with slot waveguide array for sensing,” J. Opt.19, 105801 (2017)

    2017

  58. [58]

    Imag- inary gauge potentials in a non-Hermitian spin-orbit coupled quantum gas,

    J. Tao, E. Mercado-Gutierrez, M. Zhao, and I. Spielman, “Imag- inary gauge potentials in a non-Hermitian spin-orbit coupled quantum gas,” Phys. Rev. Lett.136, 113401 (2026)

    2026

  59. [59]

    Dynamic signatures of non-Hermitian skin effect and topology in ultracold atoms,

    Q. Liang, D. Xie, Z. Dong, H. Li, H. Li, B. Gadway, W. Yi, and B. Yan, “Dynamic signatures of non-Hermitian skin effect and topology in ultracold atoms,” Phys. Rev. Lett.129, 070401 (2022)

    2022

  60. [60]

    Soliton dynamics in the discrete nonlinear Schr¨odinger equation,

    B. Malomed and M. I. Weinstein, “Soliton dynamics in the discrete nonlinear Schr¨odinger equation,” Phys. Lett. A220, 91 (1996)

    1996

  61. [61]

    Discrete solitons in optics,

    F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, “Discrete solitons in optics,” Phys. Rep.463, 1 (2008)

    2008

  62. [62]

    Discrete gap solitons in waveguide arrays with alternating spacings,

    R. A. Vicencio and M. Johansson, “Discrete gap solitons in waveguide arrays with alternating spacings,” Phys. Rev. A79, 065801 (2009)

    2009

  63. [63]

    M. F. S. Ferreira,Dissipative Optical Solitons(Springer Nature Switzerland, Cham, 2022)

    2022

  64. [64]

    Lump solutions and extreme waves for a variable coefficient Kadomtsev-Petviashvili equation in fluid mechanics,

    C. Hou, B. Wang, H. Triki, and Q. Zhou, “Lump solutions and extreme waves for a variable coefficient Kadomtsev-Petviashvili equation in fluid mechanics,” Phys. Lett. A556, 130813 (2025)

    2025

  65. [65]

    Versatile rogue waves in scalar, vector, and multidimen- sional nonlinear systems,

    S. Chen, F. Baronio, J. M. Soto-Crespo, P. Grelu, and D. Miha- lache, “Versatile rogue waves in scalar, vector, and multidimen- sional nonlinear systems,” J. Phys. A: Math. Theor.50, 463001 (2017)

    2017

  66. [66]

    Modulation instability-rogue wave correspon- dence hidden in integrable systems,

    S. Chen, L. Bu, C. Pan, C. Hou, F. Baronio, P. Grelu, and N. Akhmediev, “Modulation instability-rogue wave correspon- dence hidden in integrable systems,” Commun. Phys.5(2022), 10.1038/s42005-022-01076-x

    work page doi:10.1038/s42005-022-01076-x 2022

  67. [67]

    Discretiz- ing light behaviour in linear and nonlinear waveguide lattices,

    D. N. Christodoulides, F. Lederer, and Y. Silberberg, “Discretiz- ing light behaviour in linear and nonlinear waveguide lattices,” Nature424, 817 (2003)

    2003

  68. [68]

    Long-range interaction in waveguide lattices,

    A. Szameit, T. Pertsch, S. Nolte, A. T¨ unnermann, and F. Led- erer, “Long-range interaction in waveguide lattices,” Phys. Rev. A77, 043804 (2008)

    2008

  69. [69]

    Waveguide-lattice-based architecture for multichannel optical transformations,

    N. Skryabin, I. Dyakonov, M. Y. Saygin, and S. Kulik, “Waveguide-lattice-based architecture for multichannel optical transformations,” Opt. Express29, 26058 (2021)

    2021

  70. [70]

    A tunable narrow single-mode bandpass filter using graphene nanoribbons for THz applications,

    G. Mohammadi, A. A. Orouji, and M. Danaie, “A tunable narrow single-mode bandpass filter using graphene nanoribbons for THz applications,” Sci. Rep.14, 21217 (2024)

    2024

  71. [71]

    Programmable quantum circuits in a large-scale photonic waveguide array,

    Y. Yang, R. J. Chapman, A. Youssry, B. Haylock, F. Lenzini, M. Lobino, and A. Peruzzo, “Programmable quantum circuits in a large-scale photonic waveguide array,” Npj Quantum Inf. 11, 19 (2025)

    2025

  72. [72]

    Observation of a topological transition in the bulk of a non-Hermitian system,

    J. M. Zeuner, M. C. Rechtsman, Y. Plotnik, Y. Lumer, S. Nolte, M. S. Rudner, M. Segev, and A. Szameit, “Observation of a topological transition in the bulk of a non-Hermitian system,” Phys. Rev. Lett.115, 040402 (2015)

    2015

  73. [73]

    Aharonov–Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields,

    S. Longhi, “Aharonov–Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields,” Opt. Lett.39, 5892 (2014)

    2014

  74. [74]

    Tunable nonreciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms,

    W. Gou, T. Chen, D. Xie, T. Xiao, T.-S. Deng, B. Gadway, W. Yi, and B. Yan, “Tunable nonreciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms,” Phys. Rev. Lett.124, 070402 (2020)

    2020

  75. [75]

    Machine-guided discovery of a real-world rogue wave model,

    D. H ¨afner, J. Gemmrich, and M. Jochum, “Machine-guided discovery of a real-world rogue wave model,” Proc. Natl. Acad. Sci. U.S.A.120, e2306275120 (2023)

    2023

  76. [76]

    A. E. Gill,Atmosphere-ocean dynamics, International geo- physics series (Academic Press, New York, 1982)

    1982

  77. [77]

    Nonlinear skin breathing modes in one- dimensional nonreciprocal mechanical lattices,

    B. M. Manda, “Nonlinear skin breathing modes in one- dimensional nonreciprocal mechanical lattices,” arXiv (2025), 10.48550/arXiv.2512.17483

    work page doi:10.48550/arxiv.2512.17483 2025