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\(N\)-soliton solutions and asymptotic analysis for a Kadomtsev-Petviashvili-Schrödinger system for water waves. (English) Zbl 1327.35338
Summary: Under investigation in this paper is a Kadomtsev-Petviashvili-Schrödinger system, which describes the long waves in shallow water. Integrability study has been made through the Painlevé test. Via the Hirota method, the bilinear form and \(N\)-soliton solutions are obtained with an auxiliary variable. Collision of two solitons is found to be elastic by means of the asymptotic analysis. From the graphical descriptions of the two- and three-soliton solutions, it is found that both the bright and dark solitons collide with one another without any change in the physical quantities except for some small phase shifts during the process of each collision.

MSC:
35Q51 Soliton equations
68W30 Symbolic computation and algebraic computation
Software:
SYMMGRP
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