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Traveling waves for an integrable higher order KDV type wave equations. (English) Zbl 1192.37100
Summary: Using the method of planar dynamical systems to a higher order wave equations of KdV type, the existence of smooth and nonsmooth solitary wave, kink wave and uncountably infinite many periodic wave solutions is proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some spatial conditions, the exact explicit parametric representations of solitary wave solutions are determined.

MSC:
37K40Soliton theory, asymptotic behavior of solutions
34C05Location of integral curves, singular points, limit cycles (ODE)
35Q53KdV-like (Korteweg-de Vries) equations
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25Solitary waves (inviscid fluids)
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