Bifurcations of travelling wave solutions in a new integrable equation with peakon and compactons

DOI10.1016/j.chaos.2005.04.020zbMath1094.35109OpenAlexW2012513185MaRDI QIDQ813753

Wei Xu, Wei Li, Jianwei Shen

Publication date: 13 February 2006

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2005.04.020

zbMATH Keywords

travelling wavesbifurcationCamassa-Holm equationcompactonDegasperis-Procesi equationpeakon

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Bifurcations in context of PDEs (35B32)

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Cites Work

• Unnamed Item
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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. I: Compactons and peakons
• Convergence of solitary-wave solutions in a perturbed bi-Hamiltonian dynamical system. II: Complex analytic behavior and convergence to non-analytic solutions
• Travelling wave solutions in the generalized Hirota-Satsuma coupled KdV system
• Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation
• Bifurcations of smooth and non-smooth travelling wave solutions of the Degasperis-Procesi equation
• Traveling wave solutions for a class of nonlinear dispersive equations
• Bifurcations of travelling wave solutions for the generalized Kadomtsev-Petviashvili equation
• Travelling wave solutions in a model of the helix polypeptide chains
• Bifurcations of travelling wave solutions for the generalization form of the modified KdV equation
• Perturbative symmetry approach
• An integrable shallow water equation with peaked solitons
• Smooth and non-smooth traveling waves in a nonlinearly dispersive equation