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

TL;DR

This paper derives exact solutions and conservation laws for the (2+1)-dimensional Boiti-Leon-Pempinelli system, revealing complex wave phenomena and advancing understanding of water wave dynamics through symmetry analysis and numerical simulations.

Contribution

It introduces new exact solutions and conservation laws for the system using Lie symmetry analysis and multiplier methods, including nonlocal conservation laws.

Findings

Discovery of various wave solutions like solitons and kinks

Numerical simulations showing physical wave behaviors

Construction of local and nonlocal conservation laws

Abstract

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.