  In this article we obtain exact solutions of (2+1)-dimensional
Boiti-Leon-Pempinelli system of nonlinear partial differential equations 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 one-dimensional optimal subalgebra which involves
some arbitrary functions of spatial variables. Several new exact solutions are
obtained by symmetry reduction using each of the optimal subalgebra. We then
study the physical behavior of some exact solutions by numerical simulations
and observed many interesting phenomena such as traveling waves, lump type
solitons, kink and anti-kink type solitons, breather solitons, singular kink
type solitons and etc. We construct several conservation laws of the system by
using multipliers method. As an application, we study the nonlocal conservation
laws of the system by constructing potential systems and appending gauge
constraints.
