Nonlinear Sciences
They replace psi classes while keeping integrability, establish Miura links to Dubrovin-Zhang and ramification hierarchies, and give a short
· “Beyond descendants: integrable observables for cohomological field theories”
Twelve standard forms are obtained, including new quartic and quintic examples, for use in the Painlevé equivalence problem.
· “Modified Painlev\'e systems with meromorphic solutions for polynomial Hamiltonians of all degrees”
Idealized model proves existence and positive measure; real-table odds remain unobservably small
Confidence threshold sets cluster count; opinion-weighted attraction decides spatial merge or separation
A Poisson-bracket Lanczos algorithm supplies an early-time proxy and resolves LMG scrambling shell by shell.
Small hidden-state variations are structured and necessary; suppressing them outside a large radius blocks recovery.
End-of-channel spectral shifts recover hidden wave-field shapes even under noise, enabling soliton tomography
Lie-Scheffers structure plus mean-field coupling yields closed macroscopic equations fixed by γ=d(n-m) constants.
· “Lie Meets Network Dynamics: Exact Macroscopic Reductions (Finite Systems)”
A Goldilocks zone of intermediate pulse lengths triggers the most repeated large transients in an excitable carbon-cycle model.
· “Modeling the response of the marine carbon cycle to extreme CO₂ injection events”
One order parameter tells you which structures must form and what resolution you need
· “Coherence as Thermodynamic Organization: Toward a Non-Equilibrium Turbulence Theory”
Cold extremes thicken and the temperature field loses latitudinal phase lock as the system nears escape.
Exciton-reservoir dynamics, not waveguide geometry, drive the split and match Gross-Pitaevskii runs.
· “Mode-locking instability and multiple soliton formation in GaN polariton waveguide cavities”
Four-wave mixing amplifies a linearly stable harmonic until it dominates the peak spectrum
· “Exact vector Akhmediev breathers dominated by a linearly stable frequency”
A sign change in a spatial reparametrization turns exact nonlocal NLS and MKdV solutions into multi-valued wave profiles.
· “Loop-type geometric folding of exact solutions of shifted nonlocal NLS and MKdV equations”
Delay-free reduction predicts bistability and intermediate states better than pairwise phase lags
· “Higher-order interactions for controlling time-delayed Kuramoto model”
In obstacle-rich drone migration, the coupled Bloch-type architecture restores spatial clusters faster than memoryless baselines.
· “Self-Healing Coordination in Cognitive Swarm Agents with Bloch-Type Perceptual Memory”
Causal emergence of the low-dimensional code tracks OOD performance in nets and mouse CA1
· “Emergent Generalization by Representation Learning in Artificial Neural Networks”
Median domain density jumps by 0.089 while still scaling as a square-root power law
· “Revisiting the non-equilibrium phase transitions of the continuous-trait Axelrod model”
Exact solutions in a cubic-quintic medium stay stable under strong modulational kicks
· “Stabilization of two-dimensional optical continuous-wave states by a potential trough”
One autocatalytic term yields a fundamental plus an evenly spaced harmonic ladder in both simulation and BZ experiments
· “Chemical Frequency Combs in Reaction-Diffusion Oscillators”
Non-unique elimination multiplies each continuous model into four conjugate-symmetric systems with explicit solitons
· “Discrete Gerdjikov-Ivanov models and their higher-order counterparts from the Cauchy matrix scheme”
A complement to bifurcation diagrams that tracks finite shocks and multistability without expert branch-hunting.
· “Global continuation as a complement to traditional continuation and bifurcation analysis”
Baxter's 8-vertex R-matrix is rewritten as free-energy derivatives of the modified DKP hierarchy
· “Dispersionless modified DKP hierarchy as the Yang-Baxter equation”
Gaussian clusters grow from the center; uniform ones merge from the edges, flipping grid-style robustness
· “Paths to synchronization in the Kuramoto model with inertia”
Past a critical interaction its oscillation jumps off-center and its effective mass diverges.
Four collective states meet at (K,J)=(4,2); earlier sync formula corrected
Schramm circle patterns sit on real symplectic leaves of the same system
· “Integrability of Cauchy problems for discrete conformal maps and circle patterns”
One explicit field matches local Galerkin models without using the equations
· “Manifold-adapted radial basis functions for reduced-order modelling of chaotic flows”
Recoverability tracks quadratic triad scale k/2 and shrinks under stronger forcing
· “Intrinsic Instantaneous Coarse-to-Fine Recoverability in the Lorenz-96 System”
Landscape depth and attention must both clear critical values before a cloud function stabilizes
· “A Non-Hermitian Potential Well Formalism for Conscious--Preconscious--Subliminal Processing”
Channel number and wall reflectivity jointly tune chaotic spectra from ring-like to Ginibre-like
· “Complex spacing ratio statistics in the partially open asymmetric quantum baker map”
Standard higher-order interactions emerge only under symmetry and instant transmission; break either and richer dynamics appear
· “Impact of Channel Dynamics on Higher-order Interactions of Oscillators”
Power-law spectra and six-wave resonances measured on a single classical vortex filament, confirming a decades-old prediction for energy-cas
· “Experimental evidence of Kelvin wave turbulence along a vortex core”
Targeted magnetic fields on a neuron ring convert desynchronized bands into coherent ones, producing chimera patterns never seen under prior
· “Chimera state in a neuronal network under the action of a magnetic field”
A tunable spin-current parameter enters the localization coordinate of magnetic lump solitons, anisotropically deforming their profile and,
· “Spin-current-controlled anisotropic deformation of magnetic lump solitons”
Temporal boundaries and k-gap amplification shown to share one mathematical origin, yielding four entangled pulse branches testable by HBT/H
Nonlinear transport coefficients derived from microscopic rules, with packing fields inducing traveling energy condensates.
· “Taming nonlinear energy diffusion: The case of time-crystal energy condensates”
The same cell-force law gives different macroscopic transport in 1D vs 2D, with exponents set by γ = (β − 2)/d.
· “Dimension-dependent continuum limits in tissue mechanics”
A thermodynamic inequality limits how precisely traveling waves can signal: less energy means more positional jitter, with implications for
· “Thermodynamic Limits on Reliable Signaling by Biochemical Traveling Waves”
A uniform construction extracts one conserved quantity per prime from difference-differential Lax pairs, contrasting with the rigidity over
A reset-word criterion proves Markov invariance for one BBS variant and restricts two others to Bernoulli, with phase shifts computed for G.
· “Invariant Measures for Soliton Systems Generated by Mealy Automata”
One algebraic condition makes annealed and quenched dynamics identical and maps every heterogeneous system to a homogeneous one.
· “Unified Framework for Binary-Choice Dynamics: Analysis and Applications”
Single-site records stay non-Markovian until the total particle number is learned
· “Local Markov Order and Global Inference in Many-Body Dynamics”
Long-time analysis shows exact soliton resolution for Fokas–Lenells on elliptic seeds
· “Asymptotic analysis of N-elliptic localized solutions for the Fokas--Lenells equation”
Correlated forecast errors project onto a graph-invariant consensus mode, making topology undetectable even when neighbor observation is the
KP-I equation admits wave-kinetic thermalization to Rayleigh-Jeans states, challenging the dogma that integrable systems cannot equilibrate.
· “Wave Kinetics and Thermalization in Kadomtsev-Petviashvili-I System”
A localized seed on an unstable k-gap soliton train nucleates transient spatiotemporal bursts whose peak, timing, and shape are each tunable
· “Breathing k-Gap Events and Instability on Instability in Nonlinear Photonic Time Crystals”
Negative defect spectrum and universal angular Laplacian leave only the odd-N planar sector
· “Euler Ensemble as Decaying Turbulence Attractor: Universality, Stability and Parity Classes”
Infinitely many independent conservation laws certify integrability; travelling waves give Clifford-tori limits
· “Lund--Regge Geometry and Integrability of a Generalized Konno--Oono System”
Changing how much reinforcement people need produces jumps, bistability, and memory in adoption.
They are the orbits that keep a half-period well-swapping symmetry of the classic double-well oscillator.
· “Antiperiodic orbits and spontaneous symmetry breaking in the Duffing--Holmes oscillator”
Linear impact kills the Hopf bifurcation; cycles persist even without retail herding
· “Square-Root Price Impact Is Necessary for Endogenous Manipulation Cycles in Learning-Agent Markets”
Adjoint control of the coupling matrix drives every state onto chosen trajectories, even with 8 % of edges free.
· “Steering the dynamics by controlling the temporal interaction network”
Pfaffian N-solitons of a multi-component short-pulse equation survive full discretization and drive a self-adaptive numerical mesh
· “Integrable full discretization of the multi-component short pulse equation”
Adaptive networks that couple by local chaos rates self-organize into a narrow complexity band.
· “Complexity Condensation Through Adaptive Information Exchange”
Closed-form defect densities across higher-order exceptional points follow at once, ready for circuit or photonic tests
· “Wei-Norman approach for non-Hermitian driven spin-S systems and its application to defect freezing”
Maps show secondary detuning and drive set sharp sensitivity ridges; primary detuning and damping stay smooth.
· “On the Nonlinear Sensitivity of Phononic Frequency Combs to Physical Perturbations”
Compensation laws and hidden tradeoffs appear as manifold geometry in neuron and network models.
A sharp bound on finite-gap solutions is read off the invariant polynomial without integrating the waves
· “Maximal Densities of Finite-Gap Solutions of the Sine-Gordon Equation”
Robust phenotype under noisy morphogen is a transition to specialized covariances, not mere noise suppression
An unfolding coordinate keeps the continuation regular while parameters and normal rates are corrected together.
Smooth BPS geometries show opposite chaos trends that neither side can simply export to horizons
· “Berry Picking: Random Wave Chaos Hierarchy for BPS Microstate Geometries”
Lattice disorder drives a 2D heterostructure from incomplete to fully ergodic many-body chaos, readable in optical strengths.
· “Many-body quantum chaos in excitonic spectra from first principles”
An oblique vortex-dipole test shows only a tuned equilibrium-plus-rate package keeps trajectories isotropic.
Match mean interaction strength and the asymptotic opinion marginal of gun-control and Obamacare networks is reproduced
· “From graphons to real-world networks: kinetic opinion dynamics under selective media influence”
Complete classification shows the algebra never exceeds five dimensions and yields explicit elliptic and solitary waves.
Hastings-Levitov argument in two dimensions works for both circular and cylindrical geometries.
· “Exact amplitude relations for diffusion-limited aggregation”
Adjusted equations produce hardware that matches demanded regimes and extends to small networks.
· “Electronic Bursting Neuron: design, equations and hardware implementation”
A mapping from transfer-matrix inhomogeneities produces time-periodic open circuits that stay integrable when each bulk gate is used exactly
· “Open-boundary integrable quantum circuits with different geometries”
Clustering still lowers the exponent and raises the chance of large cascades, showing topology survives dissipation.
Shear-driven stratified turbulence develops three regimes where mixing coefficient holds near 0.1 and forward transfer dominates.
· “Energy transfer, Intermittency and Mixing in Shear-Driven Stratified Turbulence”
Local approximations match linear and first-order cases exactly or with order, but miss bifurcations in second-order transitions.
· “Analysis of the asymptotic density of endogamous diploid cellular automata”
Ratio of modulus to particle number varies intricately with interaction strength because of the soliton-droplet crossover, unlike the simple
Weak-form identification inside the inverse scattering framework yields low-dimensional models that hold in perturbed regimes.
· “Learning Effective Soliton Dynamics from Scattering Data”
A spectrally degenerate pair classified as fake generates every conserved quantity via its operator algebra, showing the true-fake split is
In a phi^4 discretization without static barrier, strong lattice spacing produces reflection and negative radiation pressure via Doppler res
· “A resonance in phonons scattering off a kink in the absence of a Peierls-Nabarro potential”
Operator methods cut the equations by the number of independent constants of motion
· “Operator-theoretic approach to the partial integration of randomly coupled phase oscillators”
The explicit bound is proved sharp from the invariant polynomial and attained by suitable data.
Recurrence map shows equal-sized waves are stable but size peaks at moderate transmission due to cross-immunity
· “Immune history shapes recurrent epidemics of antigenically related variants”
The vectors satisfy properties used to derive recurrence relations and confirm eigenvalues in related ggo-invariant models.