Author:
Wang Sheng-Nan,Yu Guo-Fu,Zhu Zuo-Nong
Abstract
AbstractIn this paper, we investigate solutions of a (2+1)-dimensional sinh-Gordon equation. General solitons and (semi-)rational solutions are derived by the combination of Hirota’s bilinear method and Kadomtsev-Petviashvili hierarchy reduction approach. General solutions are expressed as $$N\times N$$
N
×
N
Gram-type determinants. When the determinant size N is even, we generate solitons, line breathers, and (semi-)rational solutions located on constant backgrounds. In particular, through the asymptotic analysis we prove that the collision of solitons are completely elastic. When N is odd, we derive exact solutions on periodic backgrounds. The dynamical behaviors of those derived solutions are analyzed with plots. For rational solutions, we display the interaction of lumps. For semi-rational solutions, we find the interaction solutions between lumps and solitons.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics