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Zbl 1203.35242
Rui, Weiguo; Chen, Can; Yang, Xinsong; Long, Yao
Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation. (English)
[J] Appl. Math. Comput. 217, No. 4, 1666-1677 (2010). ISSN 0096-3003

Summary: By using the integral bifurcation method, we study a generalized KdV equation which was first derived by Fokas from physical considerations via a methodology of Fuchssteiner. All kinds of soliton-like or kink-like wave solutions and periodic wave solutions with loop or without loop are obtained. Smooth compacton-like periodic wave solution and non-smooth periodic cusp wave solution are also obtained. Their dynamic properties are investigated and their profiles are given by mathematical software.

MSC 2000:: *35Q53 KdV-like equations
37K10 Completely integrable systems etc.
37K50 Bifurcation problems
35C08
35B10 Periodic solutions of PDE
35-04 Machine computation, programs (partial differential equations)

Keywords: generalized KdV equation; integral bifurcation method; soliton-like solution; kink-like wave solution; periodic wave solutions with loop

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Zentralblatt MATH Berlin [Germany]