Optimal system, symmetry reductions and group-invariant solutions of (2+1)-dimensional ZK-BBM equation

The present article intends to generate optimal system of one dimensional subalgebra and group-invariant solutions of ZK-BBM equation with the aid of Lie group theory. The ZK-BBM equation is long wave equation with large wavelength, which describes the water wave phenomena in nonlinear dispersive system. The infinitesimal vectors, commutative relations and invariant functions for optimal system of ZK-BBM equation are derived under invariance of Lie groups. The invariance property leads to the reduction of independent variable and leaves the system invariant. Based on the optimal system, ZK-BBM equation is transformed into ordinary differential equations by twice reductions. These ODEs are solved under parametric constraints and result into invariant solutions. The obtained solutions are analyzed physically based on their numerical simulation. Consequently, elastic multisoliton, dark and bright lumps, compacton and annihilation profiles of the solutions are well presented graphically.

Automated summary

This article explores the optimal system and invariant solutions of the ZK-BBM equation using Lie group theory, which results in reduced independent variables and various solutions reflecting water wave phenomena.