Lie symmetry analysis and generalized invariant solutions of (2+1)-dimensional dispersive long wave (DLW) equations
Sachin Kumar, Amit Kumar, Harsha Kharbanda
Abstract
Abstract This present work applies the Lie group of point transformation method to construct the generalized invariant solutions for the (2+1)-dimensional dispersive long wave (DLW) equations under some constraints imposed on infinitesimal generators. In this connection, Lie point symmetries, vector fields and commutation relation for DLW system are well established and then the system is reduced into number of nonlinear ODEs through various symmetry reductions. An optimal system of one dimensional subalgebras of the Lie invariance algebra is formed. We exhaustively carry out symmetry reductions on the basis of these subalgebras. All the obtained solutions are more general in terms of arbitrary functions, and completely different from the previous work of the Sharma et al 2019, Phys. Scr. (Physica Scripta, 2019). Wherever possible, the relative comparison of our findings with the previous work is exhibited. Furthermore, we discuss the dynamic behavior of general solutions like annihilation of single soliton, nonlinear wave profile, curved shaped multisoliton and annihilation of doubly soliton through their evolutionary profiles.