Generalized solitary waves and fronts
نویسندگان
چکیده
Generalized solitary waves arise in many physical systems, including water waves with surface tension and multi-layered fluids [7,19,21,22]. They are nonlinear long waves consisting of a localized central core and periodic non-decaying oscillations extending to infinity. They arise whenever there is a resonance between a linear long wave speed of one wave mode in the system and a wave speed with a finite wavenumber of another mode. They have been proved to exist in specific parameter regimes, and are often conveniently modelled by perturbed Korteweg–de Vries (KdV) equations, or by coupled KdV systems [8,14].
منابع مشابه
Interfacial waves with free-surface boundary conditions: an approach via a model equation
In a two-uid system where the lower uid is bounded below by a rigid bottom and the upper uid is bounded above by a free surface, two kinds of solitary waves can propagate along the interface and the free surface: classical solitary waves characterized by a solitary pulse or generalized solitary waves with nondecaying oscillations in their tails in addition to the solitary pulse. The classical s...
متن کاملGeneralized Internal Solitary Waves and Fronts
It was shown in [1] that waves in a two-layer system with free-surface boundary conditions (or in a three-layer system) can be modelled by a system of two coupled long wave equations. The study of the resonance between a solitary wave of one of the two equations and a copropagating periodic wave of the other equation is carried out numerically. The resulting wave is a generalized solitary wave....
متن کاملStability and Evolution of Solitary Waves in Perturbed Generalized Nonlinear Schrödinger Equations
In this paper, we study the stability and evolution of solitary waves in perturbed generalized nonlinear Schrödinger (NLS) equations. Our method is based on the completeness of the bounded eigenstates of the associated linear operator in L2 space and a standard multiple-scale perturbation technique. Unlike the adiabatic perturbation method, our method details all instability mechanisms caused b...
متن کاملThe symplectic Evans matrix, and the instability of solitary waves and fronts with symmetry
Hamiltonian evolution equations which are equivariant with respect to the action of a Lie group are models for physical phenomena such as oceanographic ows, optical bres and atmospheric ows, and such systems often have a wide variety of solitary wave or front solutions. In this paper, we present a new symplectic framework for analyzing the spectral problem associated with the linearization abou...
متن کامل