Ginzburg–Landau models of nonlinear electric transmission networks

E Kengne, WM Liu, LQ English, BA Malomed - Physics Reports, 2022 - Elsevier
Abstract Complex Ginzburg–Landau (CGL) equations serve as canonical models in a great
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …

Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws

GA El, MA Hoefer, M Shearer - SIAM Review, 2017 - SIAM
We consider two physically and mathematically distinct regularization mechanisms of scalar
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …

Dispersive shock waves and modulation theory

GA El, MA Hoefer - Physica D: Nonlinear Phenomena, 2016 - Elsevier
There is growing physical and mathematical interest in the hydrodynamics of
dissipationless/dispersive media. Since GB Whitham's seminal publication fifty years ago …

Soliton gas in integrable dispersive hydrodynamics

A El Gennady - Journal of Statistical Mechanics: Theory and …, 2021 - iopscience.iop.org
We review the spectral theory of soliton gases in integrable dispersive hydrodynamic
systems. We first present a phenomenological approach based on the consideration of …

Negative-mass hydrodynamics in a spin-orbit–coupled bose-einstein condensate

MA Khamehchi, K Hossain, ME Mossman, Y Zhang… - Physical review …, 2017 - APS
A negative effective mass can be realized in quantum systems by engineering the
dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently …

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

MJ Ablowitz, JT Cole, GA El… - Studies in Applied …, 2023 - Wiley Online Library
The mathematical description of localized solitons in the presence of large‐scale waves is a
fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear …

Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation

M Girotti, T Grava, R Jenkins… - … on Pure and Applied …, 2023 - Wiley Online Library
We analyse the case of a dense modified Korteweg–de Vries (mKdV) soliton gas and its
large time behaviour in the presence of a single trial soliton. We show that the solution can …

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

GA El, EG Khamis, A Tovbis - Nonlinearity, 2016 - iopscience.iop.org
We propose a novel, analytically tractable, scenario of the rogue wave formation in the
framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the …

Resonant radiation shed by dispersive shock waves

M Conforti, F Baronio, S Trillo - Physical Review A, 2014 - APS
We analyze resonant radiation emitted by dispersive shock waves owing to higher-order
dispersive corrections of the leading term in the defocusing nonlinear Schrödinger equation …

Solitonic dispersive hydrodynamics: theory and observation

MD Maiden, DV Anderson, NA Franco, GA El… - Physical review …, 2018 - APS
Ubiquitous nonlinear waves in dispersive media include localized solitons and extended
hydrodynamic states such as dispersive shock waves. Despite their physical prominence …