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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) Zbl 1235.35259

Math. Probl. Eng. 2011, Article ID 810217, 23 p. (2011).
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.

Cited in 9 Documents

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35B32 Bifurcations in context of PDEs

Keywords:

bifurcation method; KdV equation
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\textit{L. Zhengrong} et al., Math. Probl. Eng. 2011, Article ID 810217, 23 p. (2011; Zbl 1235.35259)
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References:

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