Soliton solutions of KD system using similarity transformations method

Abstract

Present article deals with some exact solutions of (2+1)-dimensional system of coupled Konopelchenko–Dubrovsky equations. Similarity transformations method is proposed to seek the solution of the system using Lie group theory. The Lie group theory is a very strong tool by which complicated, nonlinear partial differential equations under the group transformations remains invariant. A brief review of Lie symmetries of a system of partial differential equations has been described. During the process, method reduces the number of independent variables by one. Hence, the system of partial equations reduces into a new system of ordinary differential equations. In addition, the infinitesimals after first reductions are more general than the previous established results by us (Kumar et al., 2016). Consequently, solutions so derived are more general than previously known results. We have obtained nine solutions in the explicit form, some of them are more general and some are new for the best knowledge of us. Ultimately, single solitons, multi solitons and shocks behaviour is represented graphically through the numerical simulation for physical validation of the results.