Thorough investigation of exact wave solutions in nonlinear thermoelasticity theory under the influence of gravity using advanced analytical methods

Abstract

Abstract This work aims to develop a deeper understanding of wave propagation in thermoelastic materials by deriving exact wave solutions for governing equations that account for gravity and temperature-dependent material properties. The study employs the improved modified extended tanh-function method (IMETFM) to address the coupled thermal and mechanical behaviorsin these materials, enabling the formulation of analytical solutions that capture complex wave phenomena. By extending the traditional tanh-function approach, the IMETFM allows for the derivation of diverse wave structures, including hyperbolic, polynomial, exponential, combo dark soliton, bright soliton, singular soliton, rational, and Jacobi elliptic solutions. These solutions are characterized by free parameters, offering thermoelastic in analyzing various physical scenarios. The study provides detailed graphical representations of key results, including stress tensors, displacement fields, and temperature distributions, offering visual insights into the intricate interactions within thermoelastic systems. The study’s findings emphasize the critical role of gravity and temperature dependence in shaping wave propagation and aim to advance theoretical understanding while offering potential applications in material science and engineering.