A Modified Auxiliary Method for Efficient Solutions to the (2+1)-Dimensional Variable-Coefficient Burgers’ Equation

This paper explores an innovative expansion method for solving variable-coefficient partial differential equations. Combining specific auxiliary equations with the aid of mathematical software, our method achieves notable perspectives for understanding and solving related physical problems. The validity of this method was verified through the (2+1)-dimensional variable-coefficient Burgers’ equation, and the results were visualized using three-dimensional surface plots. This study proposes an effective method for solving partial differential equations that holds broad application prospects in the field of fluid physics.