Solitons, breath-wave transitions, quasi-periodic waves and asymptotic behaviors for a (2+1)-dimensional Boussinesq-type equation
College of Mathematics, North University of China, 030051, Taiyuan, Shanxi, People’s Republic of China
Accepted: 26 July 2022
Published online: 11 August 2022
In this paper, the N-soliton solutions of a (2+1)-dimensional Boussinesq-type equation are obtained by the Hirota’s bilinear method, and one-, two-, three-soliton solutions and their clear images are given in detail. Then, one breath-wave solution and two breath-wave solution are obtained by taking the complex conjugate of soliton solutions. The transformation mechanism of the breath-waves is analyzed systematically. Through the multi-dimensional Riemann theta function and bilinear method, the quasi-periodic wave solutions are obtained. Among these periodic waves, the high-dimensional complex three-periodic waves are firstly presented, the one-periodic waves are often applied to one-dimensional models of periodic waves in shallow water, the two-periodic waves and three-periodic waves are the generalization of one-periodic waves. The asymptotic behaviors of one-, two-, three-periodic waves and the relations between periodic wave solutions and soliton wave solutions are strictly established and proved by a limiting procedure. The characteristic line method is developed to analyze the dynamical characteristics of the quasi-periodic waves.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.