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 …
variety of physical settings, such as nonlinear photonics, dynamical phase transitions …
Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
We consider two physically and mathematically distinct regularization mechanisms of scalar
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …
hyperbolic conservation laws. When the flux is convex, the combination of diffusion and …
Dispersive shock waves and modulation theory
There is growing physical and mathematical interest in the hydrodynamics of
dissipationless/dispersive media. Since GB Whitham's seminal publication fifty years ago …
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 …
systems. We first present a phenomenological approach based on the consideration of …
Negative-mass hydrodynamics in a spin-orbit–coupled bose-einstein condensate
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 …
dispersion relation. A powerful method is provided by spin-orbit coupling, which is currently …
Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics
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 …
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
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 …
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 …
framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the …
Resonant radiation shed by dispersive shock waves
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 …
dispersive corrections of the leading term in the defocusing nonlinear Schrödinger equation …
Solitonic dispersive hydrodynamics: theory and observation
Ubiquitous nonlinear waves in dispersive media include localized solitons and extended
hydrodynamic states such as dispersive shock waves. Despite their physical prominence …
hydrodynamic states such as dispersive shock waves. Despite their physical prominence …