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The bifurcations and exact traveling wave solutions for a nonlocal hydrodynamic-type system. (English) Zbl 1485.34009

This paper studies a hydrodynamic-type system taking into account nonlocal effects. The main contribution of this paper is as following: kink and anti-kink wave solutions are new solutions; the uncountably infinitely many solitary wave solutions are not mentioned in [J. Shi and J. Li, Abstr. Appl. Anal. 2014, Article ID 893279, 12 p. (2014; Zbl 1474.35541); A. Chen et al., Math. Phys. Anal. Geom. 17, No. 3–4, 465–482 (2014; Zbl 1310.34002)] before; the exact explicit parameter representation of compactons are given first. In addition, they find that pseudo-peakon is a limit solution of a family of periodic peakons.
Reviewer: Hong Li (Jiujiang)

MSC:

34A05 Explicit solutions, first integrals of ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
35C07 Traveling wave solutions
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
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References:

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