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

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.