Nonlocal conservation laws and dynamics of soliton solutions of (2 + 1)-dimensional Boiti–Leon–Pempinelli system

Abstract

In this article, we obtain several new exact solutions of (2 + 1)-dimensional Boiti–Leon–Pempinelli system of nonlinear partial differential equations (PDEs) which describes the evolution of horizontal velocity component of water waves propagating in two directions. We perform the Lie symmetry analysis to the given system and construct a one-dimensional optimal subalgebra which involves some arbitrary functions of spatial variables. Symmetry group classifications of infinite-dimensional Lie algebra for higher-dimensional system of PDEs are very interesting and rare in the literature. Several new exact solutions are obtained by symmetry reduction using each of the optimal subalgebra and these solutions have not been reported earlier in the previous studies to the best of our knowledge. We then study the dynamical behavior of some exact solutions by numerical simulations and observed many interesting phenomena, such as traveling waves, kink and anti-kink type solitons, and singular kink type solitons. We construct several conservation laws of the system by using a multiplier method. As an application, we study the nonlocal conservation laws of the system by constructing potential systems and appending gauge constraints. In fact, determining nonlocal conservation laws for higher-dimensional nonlinear system of PDEs arising from divergence type conservation laws is very rare in the literature and have huge consequences in the study of nonlocal symmetries.