Multi-Shock Wave Solution of The Damped Forced Burger Equation by Homogenization of Degree

Ranjan Barman
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Ranjan Barman: Department of Mathematics, Dinhata College, Cooch Behar, 736135, India.

International Journal of Latest Technology in Engineering, Management & Applied Science, 2025, vol. 14, issue 5, 471-478

Abstract: This article presents an investigation into the exact solution of the damped forced Burger equation with constant coefficients, utilizing a homogenization technique. By introducing a suitable change of dependent variable, the partial differential equation is transformed into a homogeneous equation of a specific degree. Subsequently, shock waves are computed employing a perturbation-like scheme that leverages linear and nonlinear operators in a finite number of steps. The study further illustrates the behavior of 2-shock and 3-shock waves under different forcing terms, providing valuable insights into the dynamics of the system. This approach enables a deeper understanding of the complex interactions between nonlinearity, damping, and external forcing in the Burger equation.

Date: 2025
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