Investigation of a novel exact wave solution structure in nonlinear thermoelasticity using modern techniques

This study introduces an enhanced methodology to investigate the complex interactions within temperature-dependent thermoelastic systems, particularly under the Dual-Phase-Lag (DPL) model. Motivated by the challenges posed by nonlinear thermoelasticity, where thermal loads significantly influence material geometry and properties, the research aims to bridge the gap in accurately modeling such phenomena. Real-world applications, including the behavior of materials under extreme thermal conditions and thermal stresses in large-scale structures, necessitate precise methodologies to capture these intricate couplings between thermal and mechanical effects. To this end, the study introduces an enhanced approach, the improved modified extended tanh function technique (IMETFT). The analysis reveals a variety of solutions, such as dark soliton, bright soliton, singular soliton, hyperbolic, rational, Jacobi elliptic, polynomial, and exponential solutions. Graphical depictions of some of the extracted solutions are included to aid readers in physically understanding the obtained solutions’ behavior and characteristics.