Conserved quantities, optimal system and explicit solutions of a (1

Introduction: The purpose of this paper is to study, a (1 + 1)-dimensional generalised coupled modified Korteweg-de Vries-type system from Lie group analysis point of view. This system is studied in the literature for the first time. The authors found this system to be interesting since it is non-decouplable and possesses higher generalised symmetries. Objectives: We look for the closed-form solutions and conservation laws of the system. Methods: Optimal system of one-dimensional subalgebras for the system was obtained and then used to perform symmetry reductions and construct group invariant solutions. Power series solutions for the system were also obtained. The system has no variational principle and as such, we employed the multiplier method and used a homotopy integral formula to derive the conserved quantities. Results: Group invariant solutions and power series solutions were constructed and three conserved vectors for the system were derived. Conclusion: The paper studies the (1 + 1)-dimensional generalised coupled modified Korteweg-de Vries-type system for the first time and constructs its exact solutions and conservation laws. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.

Automated summary

This paper studies a novel system for the first time using Lie group analysis, obtaining closed-form solutions and conservation laws. By performing symmetry reductions and constructing group invariant solutions, the paper presents group invariant solutions and power series solutions for the system. The multiplier method and homotopy integral formula were employed to derive the conserved quantities of the system.