Lie point symmetry and some new soliton-like solutions of the Konopelchenko–Dubrovsky equations

Abstract

In this paper, the infinite-dimensional symmetry groups of the ( 2 + 1 ) -dimensional Konopelchenko–Dubrovsky (KD) equation is found by the classical Lie group method. The symmetry groups are used to perform symmetry reduction and together with tanh function method we obtain soliton-like solutions. Moreover, a characterization of the corresponding Lie algebra is given.