The Solution of Two-Dimensional Coupled Burgers’ Equation by G -Double Laplace Transform

The two-dimensional coupled Burgers’ equation, a foundational partial differential equation, boasts widespread relevance across numerous scientific domains. Attaining precise solutions to this equation stands as a pivotal endeavor, fostering a comprehensive understanding of both physical phenomena and mathematical models. In this article, we underscore the paramount significance of the $G$ -double Laplace transform, a transformative mathematical tool. Leveraging this innovative technique, we furnish dependable and exact solutions, addressing both homogeneous and nonhomogeneous variants of the coupled Burgers’ equations. This approach not only delivers reliability but also serves as an invaluable instrument for delving deeper into the equation’s intricate behavior and its profound implications across diverse disciplinary landscapes.