Exact Traveling Wave Solutions and Bifurcations for a Shallow Water Equation Modeling Surface Waves of Moderate Amplitude

DOI10.1142/S0218127416501728zbMath1352.34001OpenAlexW2523238535MaRDI QIDQ2953741

Wenjing Zhu, Ji-Bin Li

Publication date: 6 January 2017

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416501728

zbMATH Keywords

exact solutionsolitary wavebifurcationshallow water equationcompactonsmooth periodic waveperiodic peakon

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Explicit solutions, first integrals of ordinary differential equations (34A05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Soliton solutions (35C08)

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Cites Work

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Traveling wave solutions of the Degasperis-Procesi equation
• Traveling surface waves of moderate amplitude in shallow water
• Traveling wave solutions of the Camassa-Holm equation
• ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS
• BIFURCATIONS AND EXACT TRAVELING WAVE SOLUTIONS OF THE GENERALIZED TWO-COMPONENT CAMASSA–HOLM EQUATION
• Classification of all travelling-wave solutions for some nonlinear dispersive equations