LIE SYMMETRIES, CONSERVATION LAWS AND EXACT SOLUTIONS FOR A CLASS OF MULTIDIMENSIONAL KDV-TYPE EQUATIONS

Abstract

This work presents a detailed Lie symmetry investigation and develops conservation laws for three multidimensional KdV-type nonlinear evolution equations in (1+1), (1+2), and (1+3) dimensions. Using the multiplier approach together with the double-reduction method, several new invariant solutions and associated conserved vectors are obtained without relying on any Lagrangian formulation. The resulting symmetries are systematically linked with their corresponding conservation laws, illustrating how invariant transformations relate to physical conservation principles. The proposed reduction strategy yields implicit and explicit exact solutions that generalize known one-dimensional mKdV models to higher-dimensional nonlinear systems. The proposed unified framework provides a systematic approach for analyzing multidimensional KdV-type equations and yields new invariant solutions that enrich the existing analytical results for nonlinear evolution equations.