The thermoelasticity deals with predicting the thermomechanical treatment of elastic solids and it is a generalization of the classical theory of elasticity and the theory of thermal conductivity. In this manuscript, the system of nonlinear partial differential equations such as the Cauchy problem which appears in a one-dimensional nonlinear coupled system of equations in the theory of thermoelasticity is studied. The homotopy analysis method was used to perform successfully the numerical calculations.
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