Exact dynamical behavior for a dual Kaup–Boussinesq system by symmetry reduction and coupled trial equations method

We propose a coupled trial equation method for a coupled differential equations system. Furthermore, according to the invariant property under the translation, we give the symmetry reduction of a dual Kaup–Boussinesq system, and then we use the proposed trial equation method to construct its exact s...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2019; no. 1; pp. 1 - 8
Main Authors Li, Wen-He, Wang, Yong
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2019
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Boussinesq equations
Difference and Functional Equations
Differential equations
Exact solution
Functional Analysis
Kaup–Boussinesq system
Mathematical analysis
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Propagation velocity
Reduction
Symmetry
The complete discrimination system for polynomial
Trial equation method
Trigonometric functions
Trial equation method
The complete discrimination system for polynomial
Kaup–Boussinesq system
Symmetry
Exact solution
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Summary:We propose a coupled trial equation method for a coupled differential equations system. Furthermore, according to the invariant property under the translation, we give the symmetry reduction of a dual Kaup–Boussinesq system, and then we use the proposed trial equation method to construct its exact solutions which describe its dynamical behavior. In particular, we get a cosine function solution with a constant propagation velocity, which shows an important periodic behavior of the system.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-019-2357-0