Related papers: Wave group evolution and interaction
We study the nonlinear modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet of given thickness and density in a basin of a constant depth. For weakly nonlinear perturbations, we derive the…
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the…
We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…
The modulation instability (MI) is responsible for the disintegration of a regular nonlinear wave train and can lead to strong localizations in a from of rogue waves. This mechanism has been studied in a variety of nonlinear dispersive…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
The present paper is the first part of a project devoted to the fractional nonlinear Schr\"{o}dinger (fNLS) equation. It is concerned with the existence and numerical generation of the solitary-wave solutions. For the first point, some…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory…
We study the applicability of the derivative nonlinear Schr\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a…
Ocean swell plays an important role in the transport of energy across the ocean, yet its evolution is still not well understood. In the late 1960s, the nonlinear Schr{\"o}dinger (NLS) equation was derived as a model for the propagation of…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the…
The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is…
The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…
The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves…
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families…
Supersonic flow of a superfluid past a slender impenetrable macroscopic obstacle is studied in the framework of the two-dimensional defocusing nonlinear Schr\"odinger (NLS) equation. This problem is of fundamental importance as a dispersive…
A nonlocal derivative NLS (nonlinear Schr\"{o}dinger) equation describes modulations of waves in a stratified fluid and a continuous limit of the Calogero--Moser--Sutherland system of particles. For the defocusing version of this equation,…
The generalized nonlinear Schr\"odinger equation with full dispersion (FDNLS) is considered in the semiclassical regime. The Whitham modulation equations are obtained for the FDNLS equation with general linear dispersion and a generalized,…