Lie group analysis of solutions of shallow water equations

Includes bibliographical references (leaves 100-101)In their paper Numerical Simulation of Two-Layer Shallow Water Flows Through Channels With Irregular Geometry, Castro et. al solves for a coupled system composed of two shallow water models with source terms involving depth and breadth functions using numerical schemes. In this paper, we consider solving for a modified version of the coupled system using the similarity method. In particular, we are interested in the resulting similarity solutions because they are unique and valuable. If they exist, they can serve as test-functions for numerical schemes. First, we describe renowned Sophus Lie's similarity method using beneficial theorems and examples. Then, we apply the method to the coupled system composed of non-friction layers and obtain similarity solutions. Lastly, we discuss the solutions