Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation

• Main Authors: Wenhao Liu, Yufeng Zhang
• Format: Article
• Language: English
• Published: SpringerOpen 2020-02-01
• Series: Advances in Difference Equations
• Subjects: ( 3 + 1 ) $(3+1)$ -dimensional B-type KP-Boussinesq equation; Bilinear method; Breathers; Lumps; Rogue waves
• Online Access: http://link.springer.com/article/10.1186/s13662-020-2493-6
• ISSN: 1687-1847

Abstract In this work, we investigate the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation, which can be used to describe the processes of interaction of exponentially localized structures. The breathers, lumps, and rogue waves of this equation are studied in detail via the Hirota bilinear method. More specifically, the general breathers, line breathers, and many kinds of interaction solutions are constructed by selecting the appropriate parameters. Based on the long wave limit method, some lumps, rogue waves, and their interaction solutions are derived. The dynamical characteristics of these solutions are vividly demonstrated through some graphical analyzes in the different planes.