https://doi.org/10.1140/epjp/s13360-020-00662-8
Regular Article
Bäcklund transformations and Riemann–Bäcklund method to a (3 + 1)-dimensional generalized breaking soliton equation
1
Department of Mathematics, North University of China, 030051, Taiyuan, Shanxi, People’s Republic of China
2
School of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, People’s Republic of China
a zhaozlhit@163.com, zhaozl@nuc.edu.cn
Received:
14
May
2020
Accepted:
31
July
2020
Published online:
9
August
2020
In this paper, the bilinear method is employed to investigate the N-soliton solutions of a (3 + 1)-dimensional generalized breaking soliton equation. Three sets of bilinear Bäcklund transformations are obtained by means of gauge transformation. The Riemann–Bäcklund method is further extended to the (3 + 1)-dimensional nonlinear integrable systems. The quasiperiodic wave solutions of the (3 + 1)-dimensional generalized breaking soliton equation are systematically analyzed. The asymptotic properties of the quasiperiodic solutions are discussed by using a limiting procedure. The one-periodic and two-periodic waves tend to the 1-soliton and 2-soliton under a small amplitude limit, respectively. The dynamical characteristics of the one- and two-periodic waves are summarized by selecting different parameters. Furthermore, we obtain some new types of the quasiperiodic wave solutions of the variable coefficient (3 + 1)-dimensional generalized breaking soliton equation. These solutions present the dynamical behaviors of C-type, anti-C-type and Z-type periodic waves moving on the background of the periodic waves of bell type.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
