Lie symmetry reductions and exact solutions of (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in shallow water

This work aims to derive symmetry reductions and exact solutions of Boiti–Leon–Manna–Pempinelli (BLMP) equation using the Lie symmetry approach. The BLMP equation is highly nonlinear integrable shallow water wave model. It describes propagation of solitary waves in shallow water. The method is based on invariance property under one parameter transformation, which ensures the reducibility of test equation and results to infinitesimals. Therefore, BLMP equation reduces independent variable and gets first symmetry reductions. A twice implementation of method transforms the BLMP equation into corresponding ordinary differential equations (ODEs). Such ODEs are determined under suitable conditions and thus, derive exact solutions. These solutions are novel and never addressed in literature. The derived solutions contain various arbitrary functions and constants, therefore significant to express rich physical structures of governing phenomena. To study physical importance of the solutions and associated phenomena, these solutions have been supplemented via numerical simulations. Thus, variety of physical structures like periodic, parabolic, multisoliton, and transition in soliton nature are analyzed systematically.