Stability of traveling wave solutions for the second-order Camassa-Holm equation

DOI10.1007/s00605-023-01828-zzbMath1529.35120OpenAlexW4322007876MaRDI QIDQ6076259

Danping Ding, Yun Li

Publication date: 23 October 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-023-01828-z

zbMATH Keywords

smoothingorbital stabilitytravelling wave solutionpseudo-conformal transformationsecond-order Camassa-Holm equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Nonlinear higher-order PDEs (35G20) Traveling wave solutions (35C07)

Cites Work

• Traveling solutions and evolution properties of the higher order Camassa-Holm equation
• Global existence for the higher-order Camassa-Holm shallow water equation
• The orbital stability of the solitary wave solutions of the generalized Camassa-Holm equation
• Orbital stability and dynamical behaviors of solitary waves for the Camassa-Holm equation with quartic nonlinearity
• Integrability of invariant metrics on the diffeomorphism group of the circle
• Geodesic flow on the diffeomorphism group of the circle
• Stability of peakons for the generalized modified Camassa-Holm equation
• Orbital stability of peakons for a modified Camassa-Holm equation with higher-order nonlinearity
• Stability of periodic peakons for the modified \(\mu \)-Camassa-Holm equation
• Stability of solitary waves for the modified Camassa-Holm equation
• Stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation
• Blow-up solution near the traveling waves for the second-order Camassa-Holm equation
• Well-posedness of higher-order Camassa-Holm equations
• Lipschitz metric for the periodic second-order Camassa-Holm equation
• Decay property of solutions near the traveling wave solutions for the second-order Camassa-Holm equation
• Traveling wave solutions of the Camassa-Holm equation
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Conservative solutions for higher-order Camassa–Holm equations
• Instability of solitons for the critical generalized Korteweg-de Vries equation
• Asymptotic stability of solitons for subcritical generalized KdV equations

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