## Some new soliton-like solutions and periodic wave solutions with loop or without loop to a generalized KdV equation.(English)Zbl 1203.35242

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:

 35Q53 KdV equations (Korteweg-de Vries equations) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K50 Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems 35C08 Soliton solutions 35B10 Periodic solutions to PDEs 35-04 Software, source code, etc. for problems pertaining to partial differential equations
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### References:

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