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The bifurcation and exact peakons, solitary and periodic wave solutions for the Kudryashov-Sinelshchikov equation. (English) Zbl 1248.35174
Summary: In this paper, the Kudryashov-Sinelshchikov equation is studied by using the bifurcation method of dynamical systems and the method of phase portraits analysis. From a dynamic point of view, the existence of peakon, solitary wave, smooth and non-smooth periodic waves is proved and the sufficient conditions to guarantee the existence of the above solutions in different regions of the parametric space are given. Also, some new exact travelling wave solutions are presented through some special phase orbits.

35Q51Soliton-like equations
35C08Soliton solutions of PDE
35C07Traveling wave solutions of PDE
35B32Bifurcation (PDE)
Full Text: DOI
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