Existence and stability of traveling waves of the fifth-order KdV equation

DOI10.1016/j.physd.2021.132872zbMath1492.35260OpenAlexW3133699240MaRDI QIDQ2077651

Amin Esfahani, Steven Paul Levandosky

Publication date: 21 February 2022

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

Full work available at URL: https://doi.org/10.1016/j.physd.2021.132872

zbMATH Keywords

stabilitysolitary wavesKdV equationground states

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items (1)

Spectral stability of multi-solitons for generalized Hamiltonian system. I: The Caudrey-Dodd-Gibbon-Sawada-Kotera equation

Cites Work

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• On the Korteweg-de Vries equation
• Lax pairs and higher order models for water waves
• Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework
• Computing the Maslov index of solitary waves. II: Phase space with dimension greater than four
• Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space
• The concentration-compactness principle in the calculus of variations. The locally compact case. I
• Stability of solitary waves of a fifth-order water wave model
• Existence of perturbed solitary wave solutions to a model equation for water waves
• The concentration-compactness principle in the calculus of variations. The locally compact case. II
• Stability and instability of standing waves for 1-dimensional nonlinear Schrödinger equation with multiple-power nonlinearity
• The existence of ground states for fourth-order wave equations
• Stability theory of solitary waves in the presence of symmetry. I
• Hamiltonian long-wave approximations to the water-wave problem
• A stability analysis of fifth-order water wave models
• Stability and instability of standing waves for one dimensional nonlinear Schrödinger equations with double power nonlinearity
• Stabilization of soliton instabilities by higher order dispersion: KdV-type equations.
• On the stability of the solitary waves to the (generalized) Kawahara equation
• Two-pulse solutions in the fifth-order KdV equation: rigorous theory and numerical approximations
• On a Class of Nonlinear Second-Order Differential Equations
• Symmetry breaking in periodic and solitary gravity-capillary waves on water of finite depth
• 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
• Existence of solitary waves for water-wave models
• Existence and Nonexistence of Solitary Wave Solutions to Higher-Order Model Evolution Equations
• A General Theory for Interactions Between Short and Long Waves
• Solitary-wave solutions to a class of fifth-order model equations
• Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations
• Linear Instability of Solitary Wave Solutions of the Kawahara Equation and Its Generalizations
• A global condition for quasi-random behavior in a class of conservative systems
• On the stability of solitary waves for the Ostrovsky equation
• Well-posedness for the fifth-order KdV equation in the energy space

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