Conserved quantities, optimal system and explicit solutions of a (1 + 1)-dimensional generalised coupled mKdV-type system

Abstract

IntroductionThe 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. ObjectivesWe look for the closed-form solutions and conservation laws of the system. MethodsOptimal 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. ResultsGroup invariant solutions and power series solutions were constructed and three conserved vectors for the system were derived. ConclusionThe 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.