Lie Symmetries and Similarity transformations for the Generalized Boiti-Leon-Pempinelli equations

TL;DR

This paper classifies Lie point symmetries and similarity solutions for the generalized Boiti-Leon-Pempinelli equations, revealing how symmetry properties vary with parameters and providing a comprehensive analysis of solutions.

Contribution

It provides a detailed classification of Lie symmetries for the equations and systematically derives similarity solutions for different parameter values.

Findings

Different numbers of Lie symmetries for various parameter values

Complete analysis of admitted Lie groups and similarity solutions

Tabular summary of results

Abstract

We perform a detailed classification of the Lie point symmetries and of the resulting similarity transformations for the Generalized Boiti-Leon-Pempinelli equations. The latter equations for a system of two nonlinear 1+2 partial differential equations of second- and third-order. The nonlinear equations depend of two parameters, namely $n$ and $m$, from where we find that for various values of these two parameters the resulting systems admit different number of Lie point symmetries. For every case, we present the complete analysis for the admitted Lie group as also we determine all the possible similarity solutions which follow from the one-dimensional optimal system. Finally, we summarize the results by presenting them in a tabular way.