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

In this work, we investigate the ( 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 bil...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2020; no. 1; pp. 1 - 12
Main Authors Liu, Wenhao, Zhang, Yufeng
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 28.02.2020
Springer Nature B.V
SpringerOpen
Subjects
( 3 + 1 ) $(3+1)$ -dimensional B-type KP-Boussinesq equation
Analysis
Bilinear method
Boussinesq equations
Breathers
Difference and Functional Equations
Functional Analysis
Lumps
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Review
Rogue waves
dimensional B-type KP-Boussinesq equation
Bilinear method
Lumps
Rogue waves
Breathers
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Summary:In this work, we investigate the ( 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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-2493-6