Author(s)

Md. Kamrujjaman¹, Asif Ahmed², Jahrul Alam²

¹Department of Mathematics, University of Dhaka, Dhaka, Bangladesh.
²Department of Mathematics and Statistics, Memorial University, St. John’s, Canada.

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 equations. 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 investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.

Nonlinear PDEs, Tan-Cot Function Method, Travelling Wave Solutions, Burg-er’s Equation, Reynolds Number, Crank-Nicolson Scheme

Kamrujjaman, M. , Ahmed, A. and Alam, J. (2019) Travelling Waves: Interplay of Low to High Reynolds Number and Tan-Cot Function Method to Solve Burger’s Equations. Journal of Applied Mathematics and Physics, 7, 861-873. doi: 10.4236/jamp.2019.74058.