Existence and orbital stability of cnoidal waves for a 1D Boussinesq equation

DOI10.1155/2007/52020zbMath1146.35076OpenAlexW2070669548MaRDI QIDQ925359

José Rául Quintero, Jaime Angulo Pava

Publication date: 3 June 2008

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/54532

zbMATH Keywords

travelling wavesBoussinesq equationorbital stabilitycnoidal wavesBenney-Luke equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45)

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Superharmonic instability for regularized long-wave models* ⋮ Solitons and periodic traveling waves for a hyperelastic dispersive equation ⋮ An instability index theory for quadratic pencils and applications ⋮ On the Cauchy problem and solitons for a class of 1D Boussinesq systems ⋮ Linear Stability of Solitary Waves for the One‐Dimensional Benney–Luke and Klein–Gordon Equations ⋮ Solitary waves of Boussinesq equation in a power law media ⋮ On the Spectral and Orbital Stability of Spatially Periodic Stationary Solutions of Generalized Korteweg-de Vries Equations ⋮ Nonlinear stability properties of periodic travelling wave solutions of the classical Korteweg-de Vries and Boussinesq equations

Cites Work

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• Stability theory of solitary waves in the presence of symmetry. II
• Stability of cnoidal waves
• Semigroups of linear operators and applications to partial differential equations
• Stability theory of solitary waves in the presence of symmetry. I
• Nonlinear stability of a one-dimensional Boussinesq equation
• Lyapunov stability of ground states of nonlinear dispersive evolution equations
• On the stability theory of solitary waves
• Total Positivity and the Stability of Internal Waves in Stratified Fluids of Finite Depth
• V.—The Periodic Lamé Functions