Exact solutions of a high-order nonlinear wave equation of Korteweg-de Vries type under newly solvable conditions. (English) Zbl 1474.35568

Summary: By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.


35Q53 KdV equations (Korteweg-de Vries equations)
35C07 Traveling wave solutions
35C08 Soliton solutions
Full Text: DOI


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