In this investigation, we examine the damped Burgers equation and the nonplanar (cylindrical and spherical) Burgers equation. We employ a successful semi-analytical approach to achieve the study’s objectives. To derive the approximate analytical solutions for these equations, we apply the ansatz method. All the derived approximations can be used to study all traveling waves, including solitary waves (SWs), shock waves (ShWs), and others described by the mentioned equations. Additionally, we use the tanh method to find an exact shock wave solution for the Burgers equation, allowing us to investigate the properties of the dissipative Burgers ShW and the nonplanar ShW using the obtained solutions. These derived approximations are valuable for researchers in plasma physics, enabling them to analyze many different structures and interpret the results of their observations and experiments.

Author: Maryam Hajij Alolowi

Published in: Ireland International Conference on Education (IICE-2024)

• Date of Conference: 28-30 October, 2024
• DOI: 10.20533/IICE.2024.10.0019
• ISBN: 978-1-913572-73-0
• Conference Location: Dún Laoghaire, Ireland