Exact solutions of the nonlinear heat conduction equation using an analytical approach

This paper presents new solutions to the nonlinear heat equation using the Exp-function method. The method employs an exponential form to construct diverse solution models, including one-soliton, two-soliton, hyperbolic, and trigonometric soliton solutions. These solutions are crucial for modeling wave phenomena in studying the stress of water surfaces. By utilizing exponential structures, the complexity of the equation is reduced, and computational efficiency is enhanced. This approach offers a robust framework for solving higher-order nonlinear partial differential equations and explains the behavior of solitons in complex systems.

کلیدواژه ها:

The exp-function approach ، The nonlinear heat equation ، Solitary and soliton solutions