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 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.

Automated summary

In this study, the (2+1)-dimensional combined Korteweg-de Vries and modified Korteweg-de Vries equation is considered for the first time. Lie symmetries are generated and corresponding transformations are used to reduce the equation to ordinary differential equations. Various soliton solutions are constructed using different techniques, and the stability of the corresponding dynamical system is investigated using phase plane theory.