Exact Solutions and Non-Traveling Wave Solutions of the (2+1)-Dimensional Boussinesq Equation

Lihui Gao, Chunxiao Guo, Yanfeng Guo and Donglong Li
Additional contact information
Lihui Gao: School of Science, China University of Mining and Technology, Beijing 100083, China
Chunxiao Guo: School of Science, China University of Mining and Technology, Beijing 100083, China
Yanfeng Guo: School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China
Donglong Li: School of Science, Guangxi University of Science and Technology, Liuzhou 545006, China

Mathematics, 2022, vol. 10, issue 14, 1-20

Abstract: By the extended ( G ′ G ) method and the improved tanh function method, the exact solutions of the (2+1) dimensional Boussinesq equation are studied. Firstly, with the help of the solutions of the nonlinear ordinary differential equation, we obtain the new traveling wave exact solutions of the equation by the homogeneous equilibrium principle and the extended ( G ′ G ) method. Secondly, by constructing the new ansatz solutions and applying the improved tanh function method, many non-traveling wave exact solutions of the equation are given. The solutions mainly include hyperbolic, trigonometric and rational functions, which reflect different types of solutions for nonlinear waves. Finally, we discuss the effects of these solutions on the formation of rogue waves according to the numerical simulation.

Keywords: (2+1)-dimensional Boussinesq equation; homogeneous equilibrium principle; extended (G?G) method; improved tanh function method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/14/2522/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/14/2522/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:14:p:2522-:d:867061

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().