The Breather-Like and Rational Solutions for the Integrable Kadomtsev-Petviashvili-Based System - Chuanjian Wang; Zhengde Dai; Changfu Liu (Advances in Mathematical Physics)
The integrable Kadomtsev-Petviashvili-based system is studied. The breather-like (a pulsating mode) and rational solutions are presented applying Hirota bilinear method and Taylor series. The intricate structures of the rational solitary wave solution are discussed mathematically and graphically. The existence conditions of three different solitary wave solution structure for the short-wave field are given by the theory of extreme value analysis. By controlling the wave number of the background plane wave we may control the the behavior of rational solitary wave. However, the shape of the rational solitary wave solution for the real long-wave field is not affected as the wave number is varied.