Journal of Applied Mathematics and Physics, 2019, 7, 861-873 http://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 DOI: 10.4236/jamp.2019.74058 Apr. 19, 2019 861 Journal of Applied Mathematics and Physics Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations Md. Kamrujjaman 1 , Asif Ahmed 2 , Jahrul Alam 2 1 Department of Mathematics, University of Dhaka, Dhaka, Bangladesh 2 Department of Mathematics and Statistics, Memorial University, St. John’s, Canada Abstract We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear eq- uations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investi- gate the effects of internal friction of a fluid via Reynolds number. By chang- ing the velocity amplitude, the nature of flows with shock wave and distur- bance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions. Keywords Nonlinear PDEs, Tan-Cot Function Method, Travelling Wave Solutions, Burger’s Equation, Reynolds Number, Crank-Nicolson Scheme 1. Introduction The wave propagation is one of the important pillar of both linear and nonlinear partial differential equations. A wave is prominently observable which is transported from one segment of the medium to another segment with a recognizable speed of propagation. The mathematical term of wave is a function of the form ( ) ( ) , utx gx ct = − where c is a constant known as wave speed and greater than zero; u is a wave function depends on two variables x and t. Here t represents the time, the initial How to cite this paper: Kamrujjaman, Md., Ahmed, A. and Alam, J. (2019) Tra- velling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations. Jour- nal of Applied Mathematics and Physics, 7, 861-873. https://doi.org/10.4236/jamp.2019.74058 Received: March 7, 2019 Accepted: April 16, 2019 Published: April 19, 2019 Copyright © 2019 by author(s) and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access