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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 on infinite intervals for ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 35Q53 KdV equations (Korteweg-de Vries equations) 35Q51 Soliton equations
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##### References:
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