Abstract
The present research is devoted to carry out Lie group classification and optimal system of one-dimensional subalgebras of KP–BBM equation. The equation describes bidirectional small amplitude and weakly dispersive long waves in nonlinear dispersive systems. The infinitesimal generators for the governing equation have been derived under invariance property of Lie groups. Thereafter, Lie symmetry analysis is used to derive commutative relations, invariant functions and optimal syatem. The symmetry reductions of KP–BBM equation are derived on basis of optimal system. Meanwhile, the twice reductions transform the KP–BBM equation into overdetermined ODEs, which lead to the exact solutions. In order to analyze the behavior of phenomena physically, the obtained solutions are extended with numerical simulation. Thus, doubly soliton, elastic multisoliton, compacton, bright and dark soliton profiles of solutions are presented to make this research physically meaningful.
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