# Similarity Solutions For The Complex Burgers' Hierarchy

## TL;DR

This paper analyzes the invariant point transformations and similarity solutions of the first four equations in the Complex Burgers' Hierarchy, reducing them to simpler forms like Abel, Riccati, and linear equations.

## Contribution

It provides a detailed symmetry analysis and reduction of the Complex Burgers' Hierarchy equations to well-known simpler differential equations.

## Key findings

- Equations are reducible to first-order Abel, Riccati, and linear equations.
- Similarity transformations facilitate the reduction process.
- The analysis enhances understanding of the structure of the hierarchy.

## Abstract

A detailed analysis of the invariant point transformations for the first four partial differential equations which belong to the Complex Burgers` Hierarchy is performed. Moreover, a detailed application of the reduction process through the Lie point symmetries is presented while we construct similarity solutions. We conclude that the differential equations of our consideration are reduced to first-order equations such as the Abel, Riccati and to a linearisable second-order differential equation by using similarity transformations.