Tootfinder

Quasi-continuum approximations for nonlinear dispersive waves in general discrete conservation laws
Su Yang
https://arxiv.org/abs/2509.04630 https://arxiv.…

Quasi-continuum approximations for nonlinear dispersive waves in general discrete conservation laws
In this paper, we study a non-integrable discrete lattice model which is a variant of an integrable discretization of the standard Hopf equation. Interestingly, a direct numerical simulation of the Riemann problem associated with such a discrete lattice shows the emergence of both the dispersive shock wave (DSW) and rarefaction wave (RW). We propose two quasi-continuum models which are represented by partial differential equations (PDEs) in order to both analytically and numerically capture the…

Field observation of soliton gases in the deep open ocean
Yu-Chen Lee, Sander Wahls
https://arxiv.org/abs/2510.04662 https://arxiv.org/pdf/2510.04662

Field observation of soliton gases in the deep open ocean
Soliton gases are large ensembles of random solitons with distinct characteristics arising from integrable system dynamics. They have been widely studied in theory and experiments, and were observed in natural lagoons. However, it remains an open question whether they occur naturally in the open ocean. Nonlinear ocean states containing solitons have been observed in the literature, but the dominance of solitons over other wave components required for a soliton gas has not been demonstrated. Our…

Spontaneous symmetry-breaking in the nonlinear Schr\"odinger equation on star graphs with inhomogeneities
Rahmi Rusin, Hadi Susanto
https://arxiv.org/abs/2509.02145 https:/…

Spontaneous symmetry-breaking in the nonlinear Schrödinger equation on star graphs with inhomogeneities
We investigate the nonlinear Schrödinger equation on a three-edge star graph, where each edge contains a linear localized inhomogeneity in the form of a Dirac delta linear potential. Such systems are of significant interest in studying wave propagation in networked structures, with applications in, e.g., Josephson junctions. By reducing the system to a set of finite-dimensional coupled ordinary differential equations, we derive explicit conditions for the occurrence of a symmetry-breaking bifu…

Resonant Interactions of Poincare Waves in the Shallow Water Approximation
D. A. Klimachkov, A. S. Petrosyan
https://arxiv.org/abs/2508.18333 https://arxiv…

Resonant Interactions of Poincare Waves in the Shallow Water Approximation
The paper develops a weakly nonlinear theory of Poincare waves. The nondegeneracy of the Poincare wave dispersion law leads to the presence of resonant interactions in perturbation theory. A study of the dispersion relation of Poincare waves showed that three-wave interactions are absent in the quadratic nonlinear approximation. In this paper, a linear equation of the envelope is derived. A qualitative study of the dispersion law showed the existence of four-wave interactions of Poincare waves.…

Evolution of extreme nonlinear wave fields over strongly reflective plane beaches
Jie Zhang, Michel Benoit, Saulo Mendes
https://arxiv.org/abs/2508.18278 https://

Evolution of extreme nonlinear wave fields over strongly reflective plane beaches
The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the leading parameter controlling the reflection rates and types of breakers. Although little is known about the effect of reflection rates on the formation of extreme nonlinear waves, some debate has arisen regarding whether high reflection rates enhance the non…

Tsunami Solitons Emerging from Superconducting Gap
Daisuke A. Takahashi
https://arxiv.org/abs/2508.18311 https://arxiv.org/pdf/2508.18311

Tsunami Solitons Emerging from Superconducting Gap
We propose a classical integrable system exhibiting the tsunami-like solitons with rocky-desert-like disordered stationary background. One of the Lax operator describing this system is interpretable as a Bogoliubov-de Gennes Hamiltonian in parity-mixed superconductor. The family of integrable equations is generated from this seed operator by Krichever's method, whose pure $s$-wave limit includes the coupled Schrödinger-Boussinesq hierarchy applied to plasma physics. A linearly unstable finite …

Deep Neural Networks can eliminate Spiral-wave Turbulence in Cardiac Tissue Models
Vasanth Kumar Babu, Rahul Pandit
https://arxiv.org/abs/2509.09806 https://

Deep Neural Networks can eliminate Spiral-wave Turbulence in Cardiac Tissue Models
Ventricular arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), precipitate sudden cardiac death (SCD), which is the leading cause of mortality in the industrialised world. Thus, the elimination of VT and VF is a problem of paramount importance, which is studied experimentally, theoretically, and numerically. Numerical studies use partial-differential-equation models, for cardiac tissue, which admit solutions with spiral- or broken-spiral-wave solutions that are th…

Quantized Thouless Pumping of Dark Solitons
Yu-Liang Tao, Huaxin He, Hao Lyu, Yongping Zhang, Yong Xu
https://arxiv.org/abs/2508.06881 https://arxiv.org/pd…

Quantized Thouless Pumping of Dark Solitons
Nonlinearity enables the emergence of localized waves such as solitons that maintain their shapes during propagation. Solitons are broadly classified into bright and dark solitons. While a bright soliton exhibits a density peak, a dark soliton presents as a defect on a continuous wave background. A distinctive feature of dark solitons is the abrupt phase change in their wave function, which can host Majorana zero modes in topological fermionic superfluids. Recent studies have shown that bright …

Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping
L. J. R. Bezerra Jr., W. S. Dias
https://arxiv.org/abs/2510.08781 htt…

Hubbard-like Interactions and Emergent Dynamical Regimes Between Modulational Instability and Self-Trapping
We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schrödinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We analyze how initially stable uniform distributions evolve into self-trapped (localized) regimes and the influence of a refractive index detuning selectively applied along the diagonal waveguides on this transition. This detuning effectively emulates the effect…

Crosslisted article(s) found for nlin.PS. https://arxiv.org/list/nlin.PS/new
[1/1]:
- Minimal velocity of the travelling wave solutions in two coupled FKPP equations with the global c...
O. I. Baburin, I. S. Burmistrov