Analytical wave solutions in thermoelastic media with temperature-dependent properties via IMETF method

This study delivers an in-depth analytical investigation of exact wave solutions derived within the context of the Three-Phase-Lag (3PHL) generalized thermoelasticity model, explicitly incorporating the temperature dependence of material properties. By applying the Improved Modified Extended Tanh Function (IMETF) method, the research addresses the governing equations that describe the coupled interaction between thermal and mechanical fields in solids. A central feature of this work is the inclusion of temperature-sensitive material parameters, which play a crucial role in modifying thermoelastic responses under a variety of thermal and mechanical loading scenarios. Unlike traditional approaches, the IMETF method extends the classical tanh-function technique by introducing a more flexible solution structure capable of capturing a richer set of waveforms. This improved methodology facilitates the derivation of diverse exact analytical solutions, each governed by distinct free parameters. These include hyperbolic, singular hyperbolic, exponential, Weierstrass elliptic, and bell-shaped solitary wave solutions. Each solution class offers unique physical insights into wave propagation behavior within temperature-dependent thermoelastic media. The analytical results not only deepen the theoretical understanding but also uncover critical features of wave interaction, dispersion, and attenuation in materials governed by the 3PHL model. To further support and illustrate these findings, the paper includes detailed graphical visualizations of key physical quantities such as stress tensor components, displacement fields, and temperature distributions. These visual results serve to highlight the influence of the temperature dependence on the wave dynamics.