Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation
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 v...
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SpringerOpen
2020-02-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-020-2493-6 |
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doaj-cb11cf69109d440aaa2a5c09ade91aec2020-11-25T00:35:04ZengSpringerOpenAdvances in Difference Equations1687-18472020-02-012020111210.1186/s13662-020-2493-6Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equationWenhao Liu0Yufeng Zhang1School of Mathematics, China University of Mining and TechnologySchool of Mathematics, China University of Mining and TechnologyAbstract 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.http://link.springer.com/article/10.1186/s13662-020-2493-6( 3 + 1 ) $(3+1)$ -dimensional B-type KP-Boussinesq equationBilinear methodBreathersLumpsRogue waves |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Wenhao Liu Yufeng Zhang |
| spellingShingle |
Wenhao Liu Yufeng Zhang Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation Advances in Difference Equations ( 3 + 1 ) $(3+1)$ -dimensional B-type KP-Boussinesq equation Bilinear method Breathers Lumps Rogue waves |
| author_facet |
Wenhao Liu Yufeng Zhang |
| author_sort |
Wenhao Liu |
| title |
Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation |
| title_short |
Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation |
| title_full |
Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation |
| title_fullStr |
Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation |
| title_full_unstemmed |
Dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional B-type Kadomtsev–Petviashvili–Boussinesq equation |
| title_sort |
dynamics of localized waves and interaction solutions for the ( 3 + 1 ) $(3+1)$ -dimensional b-type kadomtsev–petviashvili–boussinesq equation |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2020-02-01 |
| description |
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. |
| topic |
( 3 + 1 ) $(3+1)$ -dimensional B-type KP-Boussinesq equation Bilinear method Breathers Lumps Rogue waves |
| url |
http://link.springer.com/article/10.1186/s13662-020-2493-6 |
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