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Dynamics of kinky wave for \((3+1)\)-dimensional potential Yu-Toda-Sasa-Fukuyama equation. (English) Zbl 1355.35037

Summary: Exact kinky breather-wave solutions for the \((3+1)\)-dimensional potential Yu-Toda-Sasa-Fukuyama equation are obtained by using extended homoclinic test technique. Based on the kinky breather-wave solution, rational breather-wave solution is generated by homoclinic breather limit method. Some new dynamical features of kinky wave are presented, including kink degeneracy, rational breather wave is drowned or swallowed up by kinky wave in the interaction between rational breather wave and kinky wave. These results enrich the variety of the dynamics of higher dimensional nonlinear wave field.

MSC:

35C07 Traveling wave solutions
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
35Q35 PDEs in connection with fluid mechanics
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