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Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type
Chaudry Masood Khalique1,2,3, Innocent Simbanefayi1
1International Institute for Symmetry Analysis and Mathematical Modelling & Focus Area for Pure and Applied Analytics, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa.
Journal of Advanced Research
|April 12, 2021
Summary
This study introduces a novel (1+1)-dimensional generalised coupled modified Korteweg-de Vries-type system, deriving its exact solutions and conservation laws using Lie group analysis. The research provides new insights into this non-decouplable system with higher generalised symmetries.
Area of Science:
- Mathematical Physics
- Nonlinear Partial Differential Equations
- Integrable Systems
Background:
- The (1+1)-dimensional generalised coupled modified Korteweg-de Vries-type system is investigated for the first time.
- This system is notable for being non-decouplable and possessing higher generalised symmetries.
Purpose of the Study:
- To apply Lie group analysis to a novel (1+1)-dimensional generalised coupled modified Korteweg-de Vries-type system.
- To derive closed-form solutions and conservation laws for this system.
Main Methods:
- Lie group analysis was employed to obtain the optimal system of one-dimensional subalgebras.
- Symmetry reductions and group invariant solutions were constructed.
- The multiplier method and a homotopy integral formula were used to derive conserved quantities due to the absence of a variational principle.
Main Results:
- Group invariant solutions and power series solutions were successfully constructed.
- Three conserved vectors for the system were derived.
Conclusions:
- The study successfully analyzed a new (1+1)-dimensional generalised coupled modified Korteweg-de Vries-type system.
- Exact solutions and conservation laws were established for the first time for this system.
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