A (2+1)-dimensional combined KdV–mKdV equation: integrability, stability analysis and soliton solutions

In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the gov...

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Bibliographic Details
Published in:Nonlinear dynamics 2022-02, Vol.107 (3), p.2689-2701
Main Authors: Malik, Sandeep, Kumar, Sachin, Das, Amiya
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Differential equations
Dynamic stability
Dynamical Systems
Engineering
Hyperbolic functions
Integral equations
Mechanical Engineering
Ordinary differential equations
Original Paper
Solitary waves
Stability analysis
Vibration
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Summary:In this study, the (2+1)-dimensional combined Korteweg–de Vries and modified Korteweg–de Vries equation has been considered for the first time. Firstly, we check the integrability of the governing equation. Then, we generate Lie symmetries, and with the help of corresponding transformations, the governing equation has been reduced to ordinary differential equations. Further, we have constructed the dark, bright, singular and combo bright-singular soliton solutions via different techniques. The hyperbolic function method, the Kudryashov method and a new version of Kudryashov method are among these techniques. Moreover, by using phase plane theory, we investigate the stability of the corresponding dynamical system.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-07075-x