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Breather bound states in a parametrically driven magnetic wire

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A one-dimensional magnetic wire driven by an AC field can hold soliton pairs in non-stationary bound states: symmetric and asymmetric breathers, drifting bound pairs, and an intermittent state that cycles through three, five, and seven…

desk verdict Useful numerical map of LLG wire states, but the drifting-breather headline is undercut by the paper's own fast-mode cutoff and radiation-reflection concerns. read the letter →

arxiv 2411.14160 v2 pith:FIG6AZQH submitted 2024-11-21 nlin.PS

Camilo Jose Castro , Ignacio Ortega-Piwonka , Boris A. Malomed , Deterlino Urzagasti , Liliana Pedraja-Rejas , Pablo Díaz , David Laroze This is my paper · ORCID
classification nlin.PS MSC 35Q5135B3637D4582D40 PACS 05.45.-a75.78.-n
keywords Landau-Lifshitz-GilbertequationbreatherssolitonboundstatesmagneticwireparametricresonanceLyapunovexponentsmultistabilityspontaneoussymmetrybreaking
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to establish that a one-dimensional magnetic wire described by the Landau-Lifshitz-Gilbert equation, with damping balanced by a perpendicular AC drive near the 2:1 parametric resonance, supports a richer family of localized bound states than previously catalogued. It reports that two solitons can bind into stationary pairs, breathing pairs, and asymmetric breathing pairs that drift steadily, and that a small parameter window hosts an intermittent multi-soliton complex whose soliton count cycles periodically through three, five, and seven. The authors also map out where each state exists in the plane of drive amplitude and frequency detuning, quantify the drift and the largest Lyapunov exponent of each regime, and attribute the drift to radiation recoil after spontaneous symmetry breaking. If true, this extends soliton-bound-state phenomenology from the abstract parametrically driven nonlinear Schrödinger equation to a concrete magnetic-wire model, and it shows that multiple stable attractors can coexist in the same parameter window.

What carries the argument

The machine carrying the argument is the one-dimensional Landau-Lifshitz-Gilbert equation with a damping term, exchange and anisotropy energies, and a spatially uniform field containing DC and AC parts; near the 2:1 resonance this LLG model reduces to the parametrically driven damped nonlinear Schrödinger equation, which is the standard universal model for such forced dissipative systems. The numerical apparatus scans the (ν,h0) plane at fine steps, classifies states by their envelope dynamics and power-spectral density, measures center-of-mass drift by linear fits, and computes the largest Lyapunov exponent. The explanatory mechanism for the newly reported drift is radiation recoil: breathers emit low-amplitude dispersive waves, and once the bound pair's internal symmetry is broken, the left- and right-moving radiation fluxes differ, producing a net thrust.

What would settle it

Repeat the same parameter scan with a finer spatial mesh (for instance dz≤1/12), steady-state windows of at least $10^{4}$ time units, and a ring geometry with periodic boundary conditions; if the drifting asymmetric double breathers or the cyclic three-five-seven soliton state disappear or change character, they were numerical transients or boundary artifacts rather than intrinsic attractors.

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Extended reading notes

Core claim

The central claim is that the driven damped LLG wire does not merely reproduce the known single- and double-soliton states; it also hosts non-stationary bound states of its own. Specifically, the paper reports symmetric double breathers, spontaneously asymmetric double breathers that emit unequal radiation and therefore drift, fast-moving double breathers that collide with the domain edges, and a localized intermittent complex, found near (ν,h0)=(−0.20,0.45), whose soliton number repeatedly cycles through seven, five, and three as solitons collide, merge, and split. The existence and stability regions for all of these states are laid out in the (ν,h0) plane under the first Arnold tongue, and multistability is documented by the coexistence of single-soliton, double-soliton, uniform, and pattern states for the same parameters. Lyapunov analysis assigns negative exponents to the regular double-soliton states and small positive exponents to breathing states, marking the latter as weakly chaotic.

Load-bearing premise

The results rest on the assumption that the numerical scan, run on a mesh with dz≈1/6 and steady-state windows of about $10^{3}$ to 2×$10^{4}$ time units, distinguishes true long-lived attractors from transients and resolves the weak radiation that controls the breathers' drift.

Editorial extensions

If this is right

  • The (ν,h0) existence map gives concrete drive-amplitude and detuning windows where each bound-state species is the attractor reached from a symmetric two-soliton initial condition.
  • The radiation-recoil mechanism makes drift a diagnostic: an asymmetric double breather's average velocity reports the degree of internal symmetry breaking.
  • The intermittent complex is periodic on the long timescale and cycles through three-, five-, and seven-soliton configurations without global drift, so the soliton number itself becomes a dynamical variable.
  • Multistability means the same wire parameters can sustain single-soliton, double-soliton, uniform, and pattern states; the initial condition selects which one is observed.
  • Along the studied parameter line, standard double solitons have negative largest Lyapunov exponents while breathing solitons and subharmonic patterns have positive ones, so the breathing regimes are weakly chaotic rather than quasiperiodic.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because the LLG wire reduces to the parametrically driven damped nonlinear Schrödinger equation near resonance, the same family of breathing bound states and the three-five-seven soliton cycle should be sought in other parametrically driven systems, such as Faraday-wave experiments, microcavity soliton combs, or coupled pendulum arrays.
  • Editorial inference: the drifting asymmetric double breather behaves like a nano-scale 'soliton motor' whose direction and speed encode the symmetry-breaking state; it could serve as a sensitive experimental probe of radiation emission in magnetic nanowires.
  • Editorial inference: the fuzzy boundaries between breathing-state regions hint at fractal basin boundaries; a basin-entropy or initial-condition-scan study would test whether the observed multistability is organized by a riddled basin structure.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. This manuscript presents a numerical parameter-space study of a one-dimensional magnetic wire described by the Landau-Lifshitz-Gilbert equation with a DC plus AC perpendicular magnetic field. The authors scan the detuning-amplitude plane (ν, h0) with one symmetric two-soliton initial condition and classify the resulting localized states into standard solitons, breathers, double breathers, drifting asymmetric double breathers, fast-moving modes, and an intermittent multi-soliton complex exhibiting 3-5-7 soliton cycles. They characterize these states by power spectral densities, center-of-mass drift, micromagnetic energy, and the largest Lyapunov exponent, and report multistability among localized and delocalized responses.

Significance. If validated, the results would extend the known phenomenology of parametrically driven dissipative solitons from the PDNLS approximation to the full LLG model, and would document a spontaneous symmetry-breaking drift mechanism for double breathers as well as a regular intermittent multi-soliton cycle. The paper's strengths are that it uses the standard LLG equation without fitted parameters, performs a systematic scan with multiple diagnostics, and cross-checks the solver with an independent Python/Numba implementation. The main significance is contingent, however, on the numerical convergence and boundary-independence of the drifting and intermittent states, which are currently not established at the level needed for the paper's central claims.

major comments (5)
  1. [Secs. 4 and 5.3] The fast-mode exclusion criterion in Sec. 4 states that modes with drift velocity exceeding 0.005 are dismissed as artifacts of boundary collisions, yet Sec. 5.3 reports that Zone 4, the only zone with non-negligible drift, has average speeds in the range 10^-4 to 10^-1 with a maximum of 0.032. Since Zone 4 is the sole evidence for the spontaneously drifting asymmetric double breathers, this internal contradiction is load-bearing. The authors should either exclude these states by their own criterion, which would eliminate the headline phenomenon, or provide boundary-converged evidence that the drift is intrinsic, for example using longer runs, absorbing boundary conditions, or the ring geometry mentioned in the paper.
  2. [Sec. 5.5, Eq. (12)] The largest Lyapunov exponents in the range of about 10^-4 are reported without error bars or convergence tests; the value is averaged over the short window t = 1.8e4 to 2.0e4 of a single trajectory, with a sampling step of about 0.98. For a dissipative system with slow internal modulation and emitted radiation, finite-time exponents of this magnitude can be numerical artifacts or transient contamination. The claim that breathing solitons are weakly chaotic needs convergence checks with respect to the averaging window, the initial perturbation, and multiple trajectories.
  3. [Sec. 5.1, Fig. 4(a)] The phase diagram is generated from a single symmetric initial condition, Eq. (6), at each parameter point, so the colored regions are response maps for that particular initial condition rather than existence or stability regions of the states. The paper nevertheless labels Fig. 4 as 'Existence regions' and the abstract claims 'existence and stability areas.' This overstates the result; the authors should either rephrase the maps as basin-of-attraction maps for the specified initial condition or demonstrate that the states persist for other initial conditions.
  4. [Sec. 5.1, Fig. 5] The intermittent 3-5-7 soliton complex is documented at one parameter point, (ν, h0) = (-0.20, 0.45), over a steady-state window of only 10^3 time units. Because the cycle period is not reported relative to this window, a long-lived transient cannot be excluded. The 'very robust and regular' characterization requires a run covering many cycles, preferably with additional initial conditions, and a comparison with the duration of the transient stage.
  5. [Sec. 3 and Sec. 5] The steady-state diagnostics use spatial discretization dz = 1/6 and a steady-state window of 10^3 time units, but no convergence test at finer mesh or longer time is provided for the new states. This is especially relevant for the slow drift (speeds down to 10^-4) and for the weak radiation that is claimed to control the drift, because reflected radiation from the Neumann boundaries at z = ±125 can return on timescales comparable to the reported windows. Representative convergence checks for each dynamical zone would substantiate the claim that these are true attractors rather than long-lived numerical transients.
minor comments (5)
  1. [Fig. 3 caption] The caption labels panels as '3.c' and '3.d'; these should be '(c)' and '(d)' for consistency with the other panels.
  2. [Sec. 5.4 and Fig. 4 caption] The construction line is written as h0(ν) = 2.857ν + 1.729 in Fig. 4 but as h0(νh0) in Sec. 5.4; please define the parameterization consistently.
  3. [Sec. 4, PSD counting] The peak-count criterion restricts attention to peaks at ω < 3Ω, but the number of peaks will depend on the noise floor and the peak-detection algorithm; these implementation details should be stated for reproducibility.
  4. [Acknowledgments] There is a duplicated word in 'University of of Tarapacá'; it should be 'University of Tarapacá.'
  5. [Sec. 2, Eq. (5)] The critical amplitude equation is introduced with hcrit0 and then used as h_0 in the following sentence; please make the notation uniform.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the reported states are direct LLG simulations; self-citations are contextual or validation references, not load-bearing derivations.

full rationale

The paper's central claims are existence and stability regions for localized states obtained by direct numerical integration of the standard LLG equation with a stated initial condition and no fitted parameters. The diagnostics used—envelope construction, PSD peak counting, CM velocity from linear fits, micromagnetic energy, and Lyapunov exponents—are measurements applied to the simulation output rather than predictions derived from the same measurements. The self-citations to Urzagasti et al. (2012, 2013, 2014b) set the parameter values, the initial-condition family, and the numerical accuracy precedent, but none of these citations defines or forces the new double-breather, drifting, or intermittent multi-soliton states described in the paper. In particular, the claim that asymmetric double breathers drift because asymmetric radiation recoil breaks left-right balance is a physical interpretation of observed motion, not a quantity fitted into the model. The skeptical concerns about boundary reflections, transient durations, and the 0.005 fast-mode cutoff are numerical-validity risks rather than circularity: they question whether long-time dynamics are correctly resolved, but they do not show that any output was defined as its own input. Thus the derivation chain is self-contained with only minor, non-load-bearing self-citation, warranting a low score.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on standard modeling assumptions and on numerical diagnostics with several hand-set thresholds. No entities beyond the model's fields are introduced, and no parameters are fitted to force the reported states. The main fragility is the transfer of numerical accuracy from prior work and the sensitivity of the state classification to arbitrary cutoffs.

free parameters (4)
  • Fast-drift cutoff velocity = 0.005
    Threshold above which localized modes are dismissed as boundary artifacts (Sec. 4); influences which states enter the existence and CM maps.
  • ID thresholds for uniform/pattern classification = 10^-10 and 10^-2
    Thresholds used to classify states as uniform or patterns (Sec. 4).
  • PSD frequency cutoff for breathing classification = 3 Omega (peak count based)
    Only peaks below 3 Omega are counted in determining whether a state is a breather (Sec. 4).
  • Bifurcation line coefficients = 2.857 and 1.729
    The line h0 = 2.857 nu + 1.729 in Fig. 4 is chosen to traverse the existence regions; it is a diagnostic scan line, not a model fit.
assumptions (4)
  • domain assumption 1D LLG equation with the effective torque (Eqs. 1-3) models the magnetization dynamics of the wire
    The paper takes the LLG form from prior literature (Bertotti et al. 2009; Urzagasti et al. 2012) without deriving it from a Hamiltonian or micromagnetics.
  • domain assumption Neumann boundary conditions at z = +/- L with L = 125 are appropriate for the wire and do not introduce artifacts for the studied states
    The boundary conditions are imposed in Sec. 3; the paper acknowledges boundary collisions for fast states but does not quantify boundary effects on the retained states.
  • standard math The numerical scheme accuracy established in Refs. Urzagasti et al. (2014b, 2013) transfers to the present parameter range
    Section 3 states the accuracy was earlier established; no new convergence tests are reported for the new drifting and intermittent states.
  • standard math The Lyapunov exponent computed via Eq. (12) from a single perturbation converges to the true LLE within the simulation window
    The Wolf et al. method assumes a well-defined linearized evolution (Eq. 13) and sufficient averaging; the authors do not provide convergence checks.

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Pith. "Pith review of Breather bound states in a parametrically driven magnetic wire." pith.science (2026). https://pith.science/paper/FIG6AZQH

@misc{pith2026241114160,
  author       = {Pith},
  title        = {Pith review of: Breather bound states in a parametrically driven magnetic wire},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FIG6AZQH}},
  note         = {Machine review of arXiv:2411.14160}
}
read the original abstract

We report the results of systematic investigation of localized dynamical states in the model of a one-dimensional magnetic wire, which is based on the Landau-Lifshitz-Gilbert (LLG) equation. The dissipative term in the LLG equation is compensated by the parametric drive imposed by the external AC magnetic field, which is uniformly applied perpendicular to the rectilinear wire. The existence and stability of the localized states is studied in the plane of the relevant control parameters, viz., the amplitude of the driving term and the detuning of its frequency from the parametric resonance. With the help of systematically performed simulations of the LLG equation, existence and stability areas are identified in the parameter plane for several species of the localized states: stationary single- and two-soliton modes, single and double breathers, drifting double breathers with spontaneously broken inner symmetry, and multi-soliton complexes. Multistability occurs in this system. The breathers emit radiation waves (which explains their drift caused by the spontaneous symmetry breaking, as it breaks the balance between the recoil from the waves emitted to left and right), while the multi-soliton complexes exhibit cycles of periodic transitions between three-, five-, and seven-soliton configurations. Dynamical characteristics of the localized states are systematically calculated too. These include, in particular, the average velocity of the asymmetric drifting modes, and the largest Lyapunov exponent, whose negative and positive values imply that the intrinsic dynamics of the respective modes is regular or chaotic, respectively.

Figures

Figures reproduced from arXiv: 2411.14160 by the authors.

Figure 1
Figure 1. (color online) (a) The schematic of the one-dimensional wire aligned with the z-axis. The wire is made of magnetic particles subjected to the action of the perpendicular time-modulated magnetic field, h(t). As a result, the magnetization of the constituent particles (schematically denoted by white arrows in the inset), which is represented by continuous field m(z, t), is polarized according to LLG equation (1). (b–d… view at source ↗
Figure 2
Figure 2. (color online) Envelopes of different responses of the magnetic wire, defined as per Eq. (9) and plotted as [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Plots of the spatial average of my(x, t), defined as per Eq. (9) and its normalized power spectral density (PSD) for the soliton regimes displayed in [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: (color online) (a) Existence regions in the (ν, h0) parameter plane. The regions are found for the following six states: simple solitons (1–pink), breather solitons (2–purple), double solitons (3–orange), double breather solitons (4–red), fast-moving localized structur…
Figure 5
Figure 5. Figure 5: (color online) The response of the system for [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: (color online) Dynamical indicators related to the center of mass (CM) of the soliton patterns, in the [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Bifurcation diagrams plotted along the line [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

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Works this paper leans on

26 extracted references · 20 canonical work pages

  1. [8]

    Clerc, Saliya Coulibaly, and David Laroze

    Marcel G. Clerc, Saliya Coulibaly, and David Laroze. Parametrically driven instability in quasi-reversal systems. International Journal of Bifurcation and Chaos, 19(10):3525–3532, 2009a. doi:10.1142/S0218127409024967. URL https://doi.org/10.1142/S0218127409024967. Atsushi Okamura and Hidetoshi Konno. Resonant breakup of soliton in parametrically driven no...

    work page doi:10.1142/s0218127409024967

  2. [14]

    LI Reyes, LM Pérez, L Pedraja-Rejas, P Díaz, J Mendoza, J Bragard, MG Clerc, and D Laroze

    doi:10.1143/jpsj.72.1360. LI Reyes, LM Pérez, L Pedraja-Rejas, P Díaz, J Mendoza, J Bragard, MG Clerc, and D Laroze. Characterization of faraday patterns and spatiotemporal chaos in parametrically driven dissipative systems. Chaos, Solitons & Fractals, 186:115244,

    work page doi:10.1143/jpsj.72.1360

  3. [18]

    URL https: //link.aps.org/doi/10.1103/PhysRevE.77.056209

    doi:10.1103/PhysRevE.77.056209. URL https: //link.aps.org/doi/10.1103/PhysRevE.77.056209. Marcel G. Clerc, Saliya Coulibaly, and David Laroze. Nonvariational ising-bloch transition in parametrically driven sys- tems. International Journal of Bifurcation and Chaos, 19(08):2717–2726, 2009b. doi:10.1142/S0218127409024438. URL https://doi.org/10.1142/S0218127...

    work page doi:10.1103/physreve.77.056209

  4. [19]

    URL https://dx.doi

    doi:10.1209/0295-5075/104/40001. URL https://dx.doi. org/10.1209/0295-5075/104/40001. Amikam Aharoni. Introduction to the Theory of Ferromagnetism . Oxford University Press,

    work page doi:10.1209/0295-5075/104/40001

  5. [20]

    David Laroze, David Becerra-Alonso, Jason A

    doi:10.1109/TMAG.2011.2158072. David Laroze, David Becerra-Alonso, Jason A. C. Gallas, and Harald Pleiner. Magnetization dynamics under a quasiperi- odic magnetic field. IEEE Transactions on Magnetics, 48(11):3567–3570,

    work page arXiv 2011

  6. [21]

    Bertrand Kibler, Amin Chabchoub, and Heremba Bailung

    doi:10.1109/TMAG.2012.2207378. Bertrand Kibler, Amin Chabchoub, and Heremba Bailung. Peregrine Soliton and Breathers in Wave Physics: Achieve- ments and Perspectives. Frontiers Research Topics. Frontiers Media SA,

    arXiv 2012

  7. [25]

    URL https://link.aps.org/doi/10.1103/PhysRevE.102.042204

    doi:10.1103/PhysRevE.102.042204. URL https://link.aps.org/doi/10.1103/PhysRevE.102.042204. Alvar Daza, Alexandre Wagemakers, and Miguel A. F. Sanjuán. Unpredictability and basin entropy.Europhysics Letters, 141(4):43001, feb

    work page doi:10.1103/physreve.102.042204

  8. [1969]

    Dispersion-induced patterns

    P Coullet, T Frisch, and G Sonnino. Dispersion-induced patterns. Physical Review E, 49(3):2087,

    work page

Show all 26 references
  1. [1985]

    doi:https://doi.org/10.1016/0167- 2789(85)90011-9

    ISSN 0167-2789. doi:https://doi.org/10.1016/0167- 2789(85)90011-9. URL https://www.sciencedirect.com/science/article/pii/0167278985900119. Masaki Sano and Yasuji Sawada. Measurement of the lyapunov spectrum from a chaotic time series. Physical review letters, 55(10):1082,

  2. [1987]

    URL https://link.aps.org/doi/10.1103/PhysRevLett.58

    doi:10.1103/PhysRevLett.58.2209. URL https://link.aps.org/doi/10.1103/PhysRevLett.58

    doi

  3. [1989]

    URL https://api.semanticscholar.org/CorpusID:123368473

    doi:10.1143/JPSJ.58.1930. URL https://api.semanticscholar.org/CorpusID:123368473. Bruce Denardo, Brian Galvin, Alan Greenfield, Andrés Larraza, Seth Putterman, and William Wright. Observations of localized structures in nonlinear lattices: Domain walls and kinks. Phys. Rev. Le...

    1930 doi

  4. [1991]

    URL https://dx.doi.org/10.1209/0295-5075/15/2/001

    doi:10.1209/0295- 5075/15/2/001. URL https://dx.doi.org/10.1209/0295-5075/15/2/001. Michael Faraday. Xvii. on a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philosophical transactions of the Royal So...

    doi

  5. [1992]

    URL https://link.aps.org/doi/10.1103/PhysRevLett.68.1730

    doi:10.1103/PhysRevLett.68.1730. URL https://link.aps.org/doi/10.1103/PhysRevLett.68.1730. Mariana Bondila, Igor V . Barashenkov, and Mikhail M. Bogdan. Topography of attractors of the parametrically driven nonlinear schrödinger equation. Physica D: Nonlinear Phenomena , 87(1)...

    doi

  6. [1993]

    ISBN 0521437210. D. Urzagasti, A. Aramayo, and D. Laroze. Soliton–antisoliton interaction in a parametrically driven easy-plane magnetic wire. Physics Letters A , 378(35):2614–2618, 2014b. ISSN 0375-9601. doi:https://doi.org/10.1016/j.physleta.2014.07.013. URL https://www.scie...

    doi

  7. [1996]

    URL https://link.aps.org/ doi/10.1103/PhysRevE.54.5707

    doi:10.1103/PhysRevE.54.5707. URL https://link.aps.org/ doi/10.1103/PhysRevE.54.5707. A.M. Cabanas, J.A. Vélez, L.M. Pérez, P. Díaz, M.G. Clerc, D. Laroze, and B.A. Malomed. Dissipative structures in a parametrically driven dissipative lattice: Chimera, localized disorder, con...

  8. [2002]

    URL https://link.aps.org/doi/10.1103/RevModPhys.74.99

    doi:10.1103/RevModPhys.74.99. URL https://link.aps.org/doi/10.1103/RevModPhys.74.99. Nikolay N. Rosanov. Spatial Hysteresis and Optical Patterns . Springer Series in Synergetics. Springer, Berlin, Heidelberg,

    doi

  9. [2003]

    URL https: //link.aps.org/doi/10.1103/PhysRevE.68.056605

    doi:10.1103/PhysRevE.68.056605. URL https: //link.aps.org/doi/10.1103/PhysRevE.68.056605. 15 Breather bound states in a parametrically driven magnetic wire A PREPRINT Hidetsugu Sakaguchi and Boris A. Malomed. Solitary pulses and periodic waves in the parametrically driven comp...

    doi

  10. [2008]

    doi:10.1063/1.2838332. M. Lakshmanan. The fascinating world of the landau-lifshitz-gilbert equation: An overview. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, 369:1280–300, 03

    doi

  11. [2009]

    URL https://www.sciencedirect.com/science/article/pii/B9780080443164000013

    doi:10.1016/B978-0-08-044316-4.00001-3. URL https://www.sciencedirect.com/science/article/pii/B9780080443164000013. Werner Scholz and Sharat Batra. Micromagnetic modeling of ferromagnetic resonance assisted switching. Journal of Applied Physics, 103:07F539–07F539, 03

    doi

  12. [2011]

    Eric Arturo Montoya, Salvatore Perna, Yu-Jin Chen, Jordan A Katine, Massimiliano d’Aquino, Claudio Serpico, and Ilya N Krivorotov

    doi:10.1098/rsta.2010.0319. Eric Arturo Montoya, Salvatore Perna, Yu-Jin Chen, Jordan A Katine, Massimiliano d’Aquino, Claudio Serpico, and Ilya N Krivorotov. Magnetization reversal driven by low dimensional chaos in a nanoscale ferromagnet. Nature communications, 10(1):543,

    2010

  13. [2012]

    doi:10.1063/1.3672872

    ISSN 0021-8979. doi:10.1063/1.3672872. URL https://doi.org/10.1063/1.3672872. VS Shchesnovich and IV Barashenkov. Soliton–radiation coupling in the parametrically driven, damped nonlinear schrödinger equation. Physica D: Nonlinear Phenomena, 164(1-2):83–109,

    doi

  14. [2013]

    doi:10.1007/978-3-662-04792-7. L. A. Lugiato and R. Lefever. Spatial dissipative structures in passive optical systems. Phys. Rev. Lett., 58:2209–2211, May

    doi

  15. [2017]

    URL https://opg.optica.org/oe/abstract.cfm?URI=oe-25-10-11550

    doi:10.1364/OE.25.011550. URL https://opg.optica.org/oe/abstract.cfm?URI=oe-25-10-11550 . 14 Breather bound states in a parametrically driven magnetic wire A PREPRINT John W Miles. Parametrically excited solitary waves. Journal of Fluid Mechanics, 148:451–460,

    doi

  16. [2020]

    doi:10.1007/s11071-019-05433-4

    ISSN 1573-269X. doi:10.1007/s11071-019-05433-4. URL https://doi.org/10.1007/ s11071-019-05433-4 . Juan D. Bernal, Jesús M. Seoane, Juan C. Vallejo, Liang Huang, and Miguel A. F. Sanjuán. Influence of the gravitational radius on asymptotic behavior of the relativistic sitnikov ...

    doi

  17. [2023]

    URL https://dx.doi.org/10.1209/0295-5075/ acb5be

    doi:10.1209/0295-5075/acb5be. URL https://dx.doi.org/10.1209/0295-5075/ acb5be. XiaoJun Yin, LiYang Xu, and Liangui Yang. Evolution and interaction of soliton solutions of rossby waves in geophysical fluid mechanics. Nonlinear Dynamics, 111(13):12433–12445,

    doi

  18. [2789]

    URL https://www.sciencedirect.com/science/article/pii/ 016727899500126O

    doi:10.1016/0167-2789(95)00126-O. URL https://www.sciencedirect.com/science/article/pii/ 016727899500126O. Proceedings of the Conference on The Nonlinear Schrodinger Equation. I. V . Barashenkov and Yu. S. Smirnov. Existence and stability chart for the ac-driven, damped nonlin...

    doi

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