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In this article we obtain exact solutions of (2+1)-dimensionalBoiti-Leon-Pempinelli system of nonlinear partial differential equations whichdescribes the evolution of horizontal velocity component of water wavespropagating in two directions. We perform the Lie symmetry analysis to thegiven system and construct one-dimensional optimal subalgebra which involvessome arbitrary functions of spatial variables. Several new exact solutions areobtained by symmetry reduction using each of the optimal subalgebra. We thenstudy the physical behavior of some exact solutions by numerical simulationsand observed many interesting phenomena such as traveling waves, lump typesolitons, kink and anti-kink type solitons, breather solitons, singular kinktype solitons and etc. We construct several conservation laws of the system byusing multipliers method. As an application, we study the nonlocal conservationlaws of the system by constructing potential systems and appending gaugeconstraints.

Similarity reductions, new traveling wave solutions, conservation laws of (2+1)- dimensional Boiti-Leon-Pempinelli system