A direct Bäcklund transformation for a (3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation

In this paper, a Kadomtsev–Petviashvili–Boussinesq-like equation in (3+1)-dimensions is firstly introduced by using the combination of the Hirota bilinear Kadomtsev–Petviashvili equation and Boussinesq equation in terms of function f . And then a direct bilinear Bäcklund transformation of this new m...

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Bibliographic Details
Published in:Nonlinear dynamics 2017-12, Vol.90 (4), p.2263-2268
Main Authors: Yu, Jian-Ping, Sun, Yong-Li
Format: Article
Language:English
Subjects:
Automotive Engineering
Boussinesq equations
Classical Mechanics
Control
Dynamical Systems
Engineering
Mechanical Engineering
Original Paper
Transformations (mathematics)
Traveling waves
Vibration
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Summary:In this paper, a Kadomtsev–Petviashvili–Boussinesq-like equation in (3+1)-dimensions is firstly introduced by using the combination of the Hirota bilinear Kadomtsev–Petviashvili equation and Boussinesq equation in terms of function f . And then a direct bilinear Bäcklund transformation of this new model is constructed, which consists of seven bilinear equations and ten arbitrary parameters. Based on this constructed bilinear Bäcklund transformation, some classes of exponential and rational traveling wave solutions with arbitrary wave numbers are presented.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-017-3799-0