Lie Symmetries and Dynamical Behavior of Soliton Solutions of KP-BBM Equation

In this work, Lie symmetry method is employed to obtain invariant solutions of KP-BBM equation. It represents propagation of bidirectional small amplitude waves in nonlinear dispersive medium. The infinitesimal generators and their commutative relations are derived using invariance under one parameter transformation. These infinitesimal generators lead to reductions of KP-BBM equation into ODEs under two stages and thus exact solutions are constructed consisting several arbitrary constants. To analyze the physical phenomena, these solutions are expanded graphically with numerical simulation. Consequently, multisoliton, doubly soliton, compacton, soliton fusion, parabolic nature and annihilation profiles of solutions are demonstrated to validate these obtained results with physical phenomena and make the findings worthy.