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New solutions of a higher order wave equation of the KdV type. (English) Zbl 1170.35518
Summary: We use the Painlevé analysis and study a special case of a water wave equation of the KdV type. More specifically, we use the Pickering algorithm [A. Pickering, J. Math. Phys. 37, No. 4, 1894–1927 (1996; Zbl 0863.35099)] and obtain a new kind of solutions, which constitute of both algebraic and trigonometric (or hyperbolic) functions.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C05 Solutions to PDEs in closed form
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