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Some new travelling wave solutions with singular or nonsingular character for the higher order wave equation of KdV type (III). (English) Zbl 1167.34006
Summary: The integral bifurcation method was used to study the higher order nonlinear wave equations of KdV type (III), which was first proposed by Fokas. Some new travelling wave solutions with singular or nonsingular character are obtained. In particular, we obtain a peculiar exact solution of parametric type in this paper. This solution has three kinds of wave-form including solitary wave, cusp wave and loop solion under different wave velocity conditions. This phenomenon has proved that the loop soliton solution is one continuous solution, not three breaking solutions.

##### MSC:
 34B40 Boundary value problems for ODE on infinite intervals 34A05 Methods of solution of ODE 35Q53 KdV-like (Korteweg-de Vries) equations 35Q51 Soliton-like equations
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##### References:
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