On the stability of solitary-wave solutions of model equations for long waves

DOI10.1007/BF02430641zbMath0809.35095MaRDI QIDQ1337101

Jerry L. Bona, Alain Soyeur

Publication date: 29 March 1995

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

small perturbationsmall-amplitude long wavesKorteweg-de Vries-type equationsstability theory for solitary-wave solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Initial value problems for PDEs with pseudodifferential operators (35S10)

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Cites Work

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• Orbital stability of standing waves for some nonlinear Schrödinger equations
• Sufficient conditions for stability of solitary-wave solutions of model equations for long waves
• Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation
• Stability theory of solitary waves in the presence of symmetry. I
• Existence of solitary waves in higher dimensions
• The effect of dissipation on solutions of the generalized Korteweg-de Vries equation
• Instability of a class of dispersive solitary waves
• Solitary-wave solutions of nonlinear problems
• The emergence of solitons of the korteweg-de vries equation from arbitrary initial conditions
• The stability of internal solitary waves
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• Fully discrete galerkin methods for the korteweg-de vries equation
• Stability and instability of solitary waves of Korteweg-de Vries type
• Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation
• Positivity Properties and Stability of Solitary–Wave Solutions of Model Equations For Long Waves
• On the stability theory of solitary waves
• On the stability of KdV multi‐solitons
• Eigenvalues, and instabilities of solitary waves
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• Total Positivity and the Stability of Internal Waves in Stratified Fluids of Finite Depth