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Periodic loop solutions and their limit forms for the Kudryashov-Sinelshchikov equation. (English) Zbl 1264.35195

Summary: The Kudryashov-Sinelshchikov equation is studied by using the bifurcation method of dynamical systems and the method of phase portraits analysis. We show that the limit forms of periodic loop solutions contain loop soliton solutions, smooth periodic wave solutions, and periodic cusp wave solutions. Also, some new exact travelling wave solutions are presented through some special phase orbits.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35B10 Periodic solutions to PDEs
35C08 Soliton solutions
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