Exploring Wave Dynamics: Symmetry Reductions and Similarity Solutions to the (2+1) Dimensional ZK-BBM Equation

This study uses the long-established Lie symmetry approach to work out the Zakharov-Kuznetsov- Benjamin-Bona-Mahony (ZK-BBM) equation, a nonlinear partial differential equation (PDE) widely applied in modelling wave propagation across numerous materials. By distinguishing symmetries and group-invariant solutions, the ZK-BBM equation can be curtailed, and a new exact solution can be deduced. The work also probes similarity solutions to the equation, exhibiting various examples and their outcomes for wave dynamics. Eventually, conservation laws related to the ZK-BBM equation are evaluated using adjoint equations and their symmetries. The behaviour of the ZK-BBM equation and its solutions gives profound knowledge that ushers in the importance of this comprehensive study, which greatly impacts numerous study fields like quantum physics, fluid dynamics, and elasticity theory.