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Zbl 1235.35259
Zhengrong, Liu; Tianpei, Jiang; Peng, Qin; Qinfeng, Xu
Trigonometric function periodic wave solutions and their limit forms for the KdV-like and the PC-like equations. (English)
[J] Math. Probl. Eng. 2011, Article ID 810217, 23 p. (2011). ISSN 1024-123X; ISSN 1563-5147/e

Summary: We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limit forms for the KdV-like equation $u_t + a(1 + bu)uu_x + u_{xxx} = 0$, and PC-like equation $v_{tt} - v_{ttxx} - (a_1 v + a_2 v^2 + a_3 v^3)_{xx} = 0$, respectively. Via some special phase orbits, we obtain some new explicit periodic wave solutions which are called trigonometric function periodic wave solutions because they are expressed in terms of trigonometric functions. We also show that the trigonometric function periodic wave solutions can be obtained from the limits of elliptic function periodic wave solutions. It is very interesting that the two equations have similar periodic wave solutions.

MSC 2000:: *35Q53 KdV-like equations
35B10 Periodic solutions of PDE
35B32 Bifurcation (PDE)

Keywords: bifurcation method; KdV equation

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