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A similarity transformation and the decay mode solutions for three-dimensional cylindrical Kadomtsev-Petviashvili equation. (English) Zbl 1438.35382

Summary: In this paper, a similarity transformation between the solutions of three-dimensional cylindrical Kadomtsev-Petviashvili equation and the solutions of three-dimensional Kadomtsev-Petviashvili equation with constant coefficients is firstly derived, and the corresponding constraint conditions for the coefficients of the three-dimensional cylindrical Kadomtsev-Petviashvili equations are obtained. Then the exact solutions of the three-dimensional cylindrical Kadomtsev-Petviashvili equation are expressed by the similarity transformation and the solutions of the three-dimensional Kadomtsev-Petviashvili equation with constant coefficients. Lastly, four special three-dimensional cylindrical Kadomtsev-Petviashvili equations are studied, especially, the decay mode solutions of these three-dimensional cylindrical Kadomtsev-Petviashvili equations are obtained.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
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