Some more similarity solutions of the (2+1)(2+1)-dimensional BLP system

Some more similarity solutions of the coupled Boiti–Leon–Pempinelli system have been obtained by using similarity transformations method via Lie-group theory. The solutions are attained under the restrictions imposed on the functions involved in infinitesimals. Then, solutions are investigated through the graphical representation in different cases. The cases depend upon some suitable choice of arbitrary functions involved there i.e. in the solutions to get physically meaningful structures. Analytical solutions are supplemented by numerical simulations with appropriate choice of arbitrary functions and constants. Eventually, profiles show single soliton, elastic multisolitons, quasi periodic, parabolic and asymptotic nature of solutions.