Abstract:

In this paper, we present a novel application of the softmax method to solve the Chafee-Infante equation, providing various analytical solutions such as hyperbolic, trigonometric, rational, and polynomial forms. This approach simplifies solving nonlinear differential equations to obtain exact analytic solutions, particularly hyperbolic and trigonometry wave solutions by constructing the softmax function's computational model. In this study, we compare this technique to traditional methods and demonstrate its efficacy in producing more explicit and diverse solutions. The results have potential applications in fluid dynamics, nonlinear optics, and plasma physics.