Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation

DOI10.1016/S0167-2789(02)00722-4zbMath1006.35084OpenAlexW1994355333MaRDI QIDQ1852645

Filipe Oliveira

Publication date: 7 January 2003

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(02)00722-4

zbMATH Keywords

global well-posednesssolitary wave solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51)

Related Items (20)

Conservative compact difference scheme for the Zakharov–Rubenchik equations ⋮ Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation ⋮ The global existence and uniqueness of the classical solution with the periodic initial value problem for one-dimension Klein-Gordon-Zakharov equations ⋮ On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system ⋮ A radial basis function finite difference (RBF-FD) method for numerical simulation of interaction of high and low frequency waves: Zakharov-Rubenchik equations ⋮ Existence of local strong solutions for a quasilinear Benney system ⋮ Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equations ⋮ Radial basis function partition of unity procedure combined with the reduced-order method for solving Zakharov-Rubenchik equations ⋮ Uniform adiabatic limit of Benney type systems ⋮ On a coupled system of a Ginzburg–Landau equation with a quasilinear conservation law ⋮ The linear stability of shock waves for the nonlinear Schrödinger-inviscid Burgers system ⋮ On a quasilinear nonlocal Benney system ⋮ Numerical methods and simulations for the dynamics of one-dimensional Zakharov-Rubenchik equations ⋮ Adiabatic limit of the Zakharov-Rubenchik equation ⋮ New periodic solutions for a class of Zakharov equations ⋮ On long-time behavior of solutions of the Zakharov–Rubenchik/Benney–Roskes system ⋮ Two numerical methods for the Zakharov-Rubenchik equations ⋮ On the Cauchy problem describing an electron-phonon interaction ⋮ Instability of the standing waves for a Benney-Roskes/Zakharov-Rubenchik system and blow-up for the Zakharov equations ⋮ A nonlinear model describing a short wave–long wave interaction in a viscoelastic medium

Cites Work

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• Nonlinear scalar field equations. I: Existence of a ground state
• Existence and smoothing effect of solutions for the Zakharov equations
• Well-posedness for the Benney-Roskes/Zakharov-Rubenchik system
• Modulational Stability of Ground States of Nonlinear Schrödinger Equations
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Local existence of solution for the initial boundary value problem of fully nonlinear wave equation
• On the stability theory of solitary waves
• Well-posedness of the cauchy problem for the long wave-short wave resonance equations
• On a nonlinear Schrödinger equation arising in the theory of water waves

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