Lie symmetry analysis, optimal system and exact solutions of a new (2 + 1)-dimensional KdV equation

Abstract

This work attempts to apply the Lie symmetry approach to an updated (2+1)-dimensional KdV equation, recently updated in A.-M. Wazwaz, Nucl. Phys. B 954 (2020) 115009. The equation can be considered as one of the famous examples of the soliton equation. The infinitesimal generators for the governing equation have been found using the invariance property of Lie groups. The commutator table, adjoint table, invariant functions and one-dimensional optimal system of subalgebras are then derived using Lie point symmetries. Some group invariant solutions are derived based on various subalgebras, symmetry reductions and an optimal system. To demonstrate the physical acceptability of the results, the obtained solutions are evaluated using numerical simulation.