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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:
35Q53KdV-like (Korteweg-de Vries) equations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
37K50Bifurcation problems (infinite-dimensional systems)
35C08Soliton solutions of PDE
35B10Periodic solutions of PDE
35-04Machine computation, programs (partial differential equations)
References:
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