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Travelling wave solutions of the general regularized long wave equation. (English) Zbl 1472.34006

This paper studies the model of the general regularized long wave (GRLW) equation. The main contribution of this paper is to find that GRLW equation has extra kink and anti-kink wave solutions when \(p = 2n + 1\), while it’s not for \(p = 2n\). The authors give the phase diagram and obtained possible exact explicit parametric representation of the traveling wave solutions corresponding to homoclinic, hetroclinic and periodic orbits.
Reviewer: Hong Li (Jiujiang)

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
35C07 Traveling wave solutions
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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