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This https://arxiv.org/abs/2309.09001 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Bright traveling breathers in media with long-range, nonconvex dispersion
The existence and properties of envelope solitary waves on a periodic, traveling wave background, called traveling breathers, are investigated numerically in representative nonlocal dispersive media. Using a fixed point computational scheme, a space-time boundary value problem for bright traveling breather solutions is solved for the weakly nonlinear Benjamin-Bona-Mahony equation, a nonlocal, regularized shallow water wave model, and the strongly nonlinear conduit equation, a nonlocal model of …

This https://arxiv.org/abs/2305.00516 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Dissipative Soliton Resonance: Adiabatic Theory and Thermodynamics
We present the adiabatic theory of dissipative solitons (DS) of complex cubic-quintic nonlinear Ginzburg-Landau equation (CQGLE). Solutions in the closed analytical form in the spectral domain have the shape of Rayleigh-Jeans distribution for a positive (normal) dispersion. The DS parametric space forms a two-dimensional (or three-dimensional for the complex quintic nonlinearity) master diagram connecting the DS energy and a universal parameter formed by the ratio of four real and imaginary coe…

This https://arxiv.org/abs/2403.12444 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Weakly nonlinear analysis of Turing pattern dynamics on curved surfaces
Pattern dynamics on curved surfaces are ubiquitous. Although the effect of surface topography on pattern dynamics has gained much interest, there is a limited understanding of the roles of surface geometry and topology in pattern dynamics. Recently, we reported that a static pattern on a flat plane can become a propagating pattern on a curved surface [Nishide and Ishihara, Phys. Rev. Lett. 2022]. By examining reaction-diffusion equations on axisymmetric surfaces, certain conditions for the onse…

Interactions between fractional solitons in bimodal fiber cavities
Thawatchai Mayteevarunyoo, Boris A. Malomed
https://arxiv.org/abs/2402.16809 https://

Interactions between fractional solitons in bimodal fiber cavities
We report results of systematic investigation of dynamics featured by moving two-dimensional (2D) solitons generated by the fractional nonlinear Schroedinger equation (FNLSE) with the cubic-quintic nonlinearity. The motion of solitons is a nontrivial problem, as the fractional diffraction breaks the Galilean invariance of the underlying equation. The addition of the defocusing quintic term to the focusing cubic one is necessary to stabilize the solitons against the collapse. The setting present…

This https://arxiv.org/abs/2401.05261 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

On the kinks, the solitons and the shocks in discrete nonlinear transmission line
We studied lossless discrete transmission lines constructed from ideal linear inductors and nonlinear capacitors. The travelling waves with finite support in such systems are the kinks and the solitons, which speeds and profiles were calculated. We also studied lossy transmission lines. The travelling waves with finite support in such systems are the dissipative kinks and the shocks, which speeds and profiles were also calculated.

Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system
Junyuan Shi
https://arxiv.org/abs/2402.15736 https://

Turing pattern theory on homogeneous and heterogeneous higher-order temporal network system
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding network dynamics theories have been continuously enriched with the advancement of network science. Recently, time-varying feature and many-body interactions have been discovered on various and numerous networks in real world like biological and social systems, and the study of contemporary network science has gradually moved away from the historically static network …

Spiral, Core-defect and Wave break in a modified Oregonator Model
Parvej Khan, Sumana Dutta
https://arxiv.org/abs/2403.15731 https://…

Spiral, Core-defect and Wave break in a modified Oregonator Model
Target waves and spiral waves were discovered in the Belousov-Zhabotinsky (BZ) reaction around 50 years ago. Inwardly rotating spiral waves, also called the anti-spirals, were found in a BZ-AOT system about two decades ago. Many biological systems demonstrate both spiral and anti-spirals. In the glycolytic activity of yeast, anti-spirals are observed, whereas spiral waves are widely studied in the context of broken cardiac waves. In the cardiac system, only outwardly rotating normal spirals are…

Hydrodynamics of a Discrete Conservation Law
Patrick Sprenger, Christopher Chong, Emmanuel Okyere, Michael Herrmann, P. G. Kevrekidis, Mark A. Hoefer
https://arxiv.org/abs/2404.16750

Hydrodynamics of a Discrete Conservation Law
The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of solutions to this simple discrete regularization of the inviscid Burgers' equation is obtained. In addition to discrete analogues of well-known dispersive hydrodynamic solutions -- rarefaction waves (RWs) and dispersive shock waves (DSWs) -- additional unsteady so…

Third order interactions shift the critical coupling in multidimensional Kuramoto models
Ricardo Fariello, Marcus A. M. de Aguiar
https://arxiv.org/abs/2404.16715

Third order interactions shift the critical coupling in multidimensional Kuramoto models
The study of higher order interactions in the dynamics of Kuramoto oscillators has been a topic of intense recent research. Arguments based on dimensional reduction using the Ott-Antonsen ansatz show that such interactions usually facilitate synchronization, giving rise to bi-stability and hysteresis. Here we show that three body interactions shift the critical coupling for synchronization towards higher values in all dimensions, except D=2, where a cancellation occurs. After the transition, th…