Bifurcations and exact bounded travelling wave solutions for a partial differential equation

DOI10.1016/j.nonrwa.2008.11.009zbMath1181.35214OpenAlexW2065003234MaRDI QIDQ1049449

Bin He

Publication date: 12 January 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2008.11.009

zbMATH Keywords

exact solutionpartial differential equationperiodic wavepeakonbreaking waveloop solitongeneralized compacton

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Soliton equations (35Q51) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50) Traveling wave solutions (35C07) Soliton solutions (35C08)

Related Items

Explicit wave solutions and qualitative analysis of the \((1+2)\)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity ⋮ Bifurcation and exact solutions for the \((2+1)\)-dimensional conformable time-fractional zoomeron equation ⋮ Explicit kink-like and compacton-like wave solutions for a generalized KdV equation ⋮ Bounded traveling wave solutions and their relations for the generalized HD type equation ⋮ The limiting behavior of smooth periodic waves for the Degasperis-Procesi equation ⋮ Traveling waves in chains of pendula ⋮ EXPLICIT EXACT PERIODIC WAVE SOLUTIONS AND THEIR LIMIT FORMS FOR A LONG WAVES-SHORT WAVES MODEL ⋮ Periodic loop solutions and their limit forms for the Kudryashov-Sinelshchikov equation ⋮ Notes on ``Solitary wave solutions of the generalized two-component Hunter-Saxton system ⋮ Bifurcation analysis and different kinds of exact travelling wave solutions of a generalized two-component Hunter-Saxton system ⋮ Qualitative behavior and cusped solitons for a partial differential equation ⋮ Qualitative Analysis and Explicit Exact Solitary, Kink and Anti-Kink Wave Solutions of the Generalized Nonlinear Schrödinger Equation with Parabolic Law Nonlinearity ⋮ Extension on peakons and periodic cusp waves for the generalization of the Camassa-Holm equation

Cites Work

• Unnamed Item
• Peakons, solitary patterns and periodic solutions for generalized Camassa-Holm equations
• Bifurcations of travelling wave solutions for a variant of Camassa-Holm equation
• Cusp and loop soliton solutions of short-wave models for the Camassa-Holm and Degasperis-Procesi equations
• The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
• Peakons and coshoidal waves: Traveling wave solutions of the Camassa-Holm equation
• Soliton interactions for the Camassa-Holm equation
• Travelling wave solutions for a higher order wave equations of KdV type. I
• Traveling wave solutions for a class of nonlinear dispersive equations
• Peakons of the Camassa-Holm equation
• Solitons in the Camassa-Holm shallow water equation
• Travelling wave solutions for higher-order wave equations of KdV type. III
• Nonlinear asymptotic short-wave models in fluid dynamics
• The multiple-soliton solution of the Camassa-Holm equation
• Compacton-like and kink-like waves for a higher-order wave equation of Korteweg–de Vries type
• Dynamics of Director Fields
• Solitons in a nonlinear model medium
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• The Scattering Approach for the Camassa—Holm equation
• Smooth and non-smooth traveling waves in a nonlinearly dispersive equation
• The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type