Stability of multipeakons

DOI10.1016/j.anihpc.2009.02.002zbMath1171.35459arXiv0803.0261OpenAlexW3100288554MaRDI QIDQ2272081

Khaled El Dika, Luc Molinet

Publication date: 5 August 2009

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0803.0261

zbMATH Keywords

Camassa-Holm equationorbital stabilitymultipeakons

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51)

Related Items (59)

Stability of the train of \(N\) solitary waves for the two-component Camassa-Holm shallow water system ⋮ Stability of peakons of the Camassa–Holm equation beyond wave breaking ⋮ Stability of the Camassa-Holm multi-peakons in the dynamics of a shallow-water-type system ⋮ Orbital stability of periodic peakons for a new higher-order μ-Camassa–Holm equation ⋮ Orbital stability of solitary traveling waves of moderate amplitude ⋮ Local well-posedness and blow-up for a family of \(U(1)\)-invariant peakon equations ⋮ Stability of peakons and periodic peakons for a nonlinear quartic Camassa-Holm equation ⋮ Existence and uniqueness of global weak solutions of the Camassa-Holm equation with a forcing ⋮ Orbital stability of peakons for a generalized CH equation ⋮ Orbital stability of the sum of \(N\) peakons for the generalized higher-order Camassa-Holm equation ⋮ Stability of periodic peaked solitary waves for a cubic Camassa-Holm-type equation ⋮ Unnamed Item ⋮ Stability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearity ⋮ Orbital stability of a sum of solitons and breathers of the modified Korteweg–de Vries equation ⋮ Convergence analysis of the vortex blob method for the \(b\)-equation ⋮ Orbital stability of the sum of \(N\) peakons for the Dullin-Gottwald-Holm equation ⋮ Local well-posedness and stability of solitary waves for the two-component Dullin-Gottwald-Holm system ⋮ On the orbital stability of the Degasperis-Procesi antipeakon-peakon profile ⋮ Stability of peakons for the Novikov equation ⋮ Blow-up solutions and peakons to a generalized {\(\mu\)}-Camassa-Holm integrable equation ⋮ Single peaked traveling wave solutions to a generalized \(\mu\)-Novikov equation ⋮ Orbital stability of the sum of \(N\) peakons for the generalized modified Camassa-Holm equation ⋮ Energy conservation and well-posedness of the Camassa-Holm equation in Sobolev spaces ⋮ Dissipative prolongations of the multipeakon solutions to the Camassa-Holm equation ⋮ Orbital stability of pseudo-peakons for the fifth-order Camassa-Holm type equation ⋮ Orbital stability of peakons and multi-peakons for a generalized cubic-quintic Camassa-Holm type equation ⋮ Orbital stability of the trains of peaked solitary waves for the modified Camassa-Holm-Novikov equation ⋮ The well-posedness for the Camassa-Holm type equations in critical Besov spaces \(B_{p , 1}^{1 + \frac{ 1}{ p}}\) with \(1 \leq p < + \infty \) ⋮ The two-component \(\mu\)-Camassa-Holm system with peaked solutions ⋮ A remark on the stability of peakons for the Degasperis-Procesi equation ⋮ Orbital stability of two-component peakons ⋮ Dynamical stability of the train of smooth solitary waves to the generalized two-component Camassa-Holm system ⋮ Stability of periodic peakons for a nonlinear quartic \(\mu\)-Camassa-Holm equation ⋮ Stability of periodic peakons for the modified \(\mu \)-Camassa-Holm equation ⋮ Orbital stability of periodic peakons to a generalized \(\mu\)-Camassa-Holm equation ⋮ An asymptotic property of the Camassa-Holm equation ⋮ Lax integrability and the peakon problem for the modified Camassa-Holm equation ⋮ Orbital stability of the train of peakons for an integrable modified Camassa-Holm equation ⋮ The local and global existence of solutions for a generalized Camassa-Holm equation ⋮ Long time behaviour for a class of low-regularity solutions of the Camassa-Holm equation ⋮ On the low regularity solutions and wave breaking for an equation modeling shallow water waves of moderate amplitude ⋮ Stability of peakons for the generalized modified Camassa-Holm equation ⋮ An asymptotic property of the Camassa-Holm equation on the half-line ⋮ Stability in the energy space of the sum of N peakons for a modified Camassa-Holm equation with higher-order nonlinearity ⋮ Well-posedness and wave breaking of the degenerate Novikov equation ⋮ Orbital stability of floating periodic peakons for the Camassa-Holm equation ⋮ A Liouville property with application to asymptotic stability for the Camassa-Holm equation ⋮ Orbital and asymptotic stability of a train of peakons for the Novikov equation ⋮ Non-uniform dependence and well-posedness for the rotation-Camassa-Holm equation on the torus ⋮ Liouville correspondence between the modified KdV hierarchy and its dual integrable hierarchy ⋮ Orbital stability of elliptic periodic peakons for the modified Camassa-Holm equation ⋮ Orbital stability of periodic peakons for the generalized modified Camassa-Holm equation ⋮ Orbital stability of peakons for the modified Camassa-Holm equation ⋮ Asymptotic stability of peakons for the Novikov equation ⋮ A view of the peakon world through the lens of approximation theory ⋮ Orbital stability of the sum of N solitary waves for the hyperelastic-rod wave equation ⋮ The periodic Cauchy problem for a two-component non-isospectral cubic Camassa-Holm system ⋮ Stability in the energy space of the sum of \(N\) peakons for the Degasperis-Procesi equation ⋮ Stability of smooth multi-solitons for the Camassa-Holm equation

Cites Work

• Unnamed Item
• Smoothing effect of the generalized BBM equation for localized solutions moving to the right
• Stability of \(N\) solitary waves for the generalized BBM equations
• The trajectories of particles in Stokes waves
• Global conservative solutions of the Camassa-Holm equation
• A convergent numerical scheme for the Camassa-Holm equation based on multipeakons
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Stability theory of solitary waves in the presence of symmetry. I
• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Global weak solutions for a shallow water equation
• Multipeakons and the classical moment problem
• A few remarks on the Camassa-Holm equation.
• Stability of the Camassa-Holm solitons
• Stability and asymptotic stability for subcritical gKdV equations
• Stability in \(H^1\) of the sum of \(K\) solitary waves for some nonlinear Schrödinger equations
• On the scattering problem for the Camassa-Holm equation
• Inverse scattering transform for the Camassa–Holm equation
• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey
• Exponential decay of H ¹ -localized solutions and stability of the train of N solitary waves for the Camassa–Holm equation
• Particle trajectories in solitary water waves
• Orbital stability of solitary waves for a shallow water equation

This page was built for publication: Stability of multipeakons