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Zbl 1144.35461
Rui, Weiguo; He, Bin; Long, Yao; Chen, Can
The integral bifurcation method and its application for solving a family of third-order dispersive PDEs. (English)
[J] Nonlinear Anal., Theory Methods Appl. 69, No. 4, A, 1256-1267 (2008). ISSN 0362-546X

Summary: An improved method named the integral bifurcation method is introduced. In order to demonstrate its effectiveness for obtaining travelling wave solutions of the nonlinear wave equations, a family of third-order dispersive partial differential equations which were given by A. Degasperis, D. Holm and A. Hone are studied. Many integral bifurcations are obtained for different parameter conditions. By using these integral bifurcations, many travelling wave solutions such as loop soliton solutions, solitary wave solutions, cusp soliton solutions and periodic wave solutions are obtained. In particular, under the conditions $c_{1}<0,c_{2}=c_{3}=1$, a very peculiar periodic wave solution is obtained.

MSC 2000:: *35Q53 KdV-like equations
35Q51 Solitons
35B10 Periodic solutions of PDE
35A30 Geometric theory for PDE, transformations

Keywords: integral bifurcation method; A family of third-order dispersive PDEs; loop soliton; cusp soliton; peculiar periodic wave

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Zentralblatt MATH Berlin [Germany]