On the study of an extended coupled KdV system: Analytical solutions and conservation laws

Abstract

This paper aims to derive analytical solutions of an extended (2+1)-dimensional constant coefficients new coupled Korteweg-de Vries system. This will be achieved by implementing the classical symmetry method in conjunction with some simplest equation methods. The simplest equations that will be utilised includes among others the Bernoulli and Riccati equations. Furthermore, the conservation laws will be constructed through the multipliers approach, which subsequently reveals the conserved quantities. Moreover, a brief presentation of results obtained consisting of a variety of profile structures which include the kink type, bell and inverted bell shaped and singular wave solutions will be discussed.