Solution of nonlinear Burger's equation arising in longitudinal dispersion phenomena

Abstract

The present article showcases a novel approach for obtaining the approximate solution of the nonlinear Burgers' equation, a frequently occurring equation in the study of wave propagation and dispersion phenomena. The Double Power Series Method, a methodology not conventionally applied to this equation, introduces a unique analytical perspective. The method's versatility in handling two independent variables makes it particularly well-suited for addressing the complexities of the Burgers' equation, providing a comprehensive representation of fluid concentration for arbitrary distances and times. Through this novel approach, we study the intricate dynamics governing the relationship between convection and diffusion forces in longitudinal dispersion. This research not only enriches the theoretical foundation of nonlinear partial differential equations but also holds promise for practical applications across fluid dynamics, environmental engineering, and beyond. Both numerical and graphical solutions are meticulously computed through MATLAB coding, facilitating a robust physical interpretation of the results. This study contributes valuable insights into the behavior of fluids in dispersion scenarios, offering a practical approach to understanding and predicting such phenomena.