# Lie symmetry analysis for similarity reduction and solutions of (3 + 1)- dimensional Calogero-Bogoyavlenskii-Schiff equation

## TL;DR

This paper applies Lie symmetry analysis to reduce and solve the (3+1)-dimensional Calogero-Bogoyavlenskii-Schiff equation, deriving similarity solutions and exact solutions through symmetry reductions.

## Contribution

It introduces a systematic Lie group analysis approach to obtain similarity reductions and exact solutions for the (3+1)-dimensional CBS equation, including derivation of infinitesimal generators and symmetry groups.

## Key findings

- Reduced (3+1)-D CBS equation to (2+1)-D PDEs
- Further reduced PDEs to ODEs using symmetry methods
- Obtained explicit similarity solutions for the CBS equation

## Abstract

It is shown that the novel Lie group of transformations method is a competent and prominent tool in solving nonlinear partial differential equations(PDEs) in mathematical physics. Lie group analysis is used to carry out the similarity reduction and exact solutions of the (3 + 1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation. This research deals with the similarity solutions of CBS equation. We have obtained the infinitesimal generators, commutator table of Lie algebra, symmetry group and similarity reduction for the CBS equation. For the different Lie algebra, Lie symmetry method reduced (3 + 1)-dimensional CBS equation into new (2 + 1)-dimensional partial differential equations and again using Lie symmetry method these PDEs are reduced into various ordinary differential equations(ODEs).