Novel analytical wave solutions in nonlinear thermoelasticity using the IME tanh function method

Abstract

This study presents the improved Modified Extended (IME) tanh function method, utilized to analyze equations based on the Green–Naghdi (G–N II) theory thermo-elasticity. Unlike conventional methods, the proposed technique enhances the ability to derive a wide spectrum of exact solutions, making it particularly effective for capturing the complex interplay between mechanical and thermal effects in nonlinear thermoelastic systems. Nonlinear thermo-elasticity examines scenarios when a material’s characteristics and form experience substantial changes due to varying thermal stresses. This research domain is essential for understanding real-world phenomena, including material behavior at elevated temperatures, thermal stresses in extensive structures, and intricate interactions between mechanical and thermal forces. The suggested method produces a diverse array of exact solutions, encompassing exponential, polynomial, Jacobi elliptic (JE), singular soliton, and hyperbolic solutions, with distinct free parameters that have not been documented. Additionally, the study incorporates graphical depictions of diverse displacement components, temperature variations, and stress tensors.