About Exact Solutions in the Coupled Dynamical Problem of the Thermoelasticity for a Homogeneous One-dimensional Bar

Abstract

The system of second order nonlinear partial differential equations describes coupled longitudinal mechanical oscillation and temperature variation (of temperature) in an one- dimension homogeneous isotropic bounded solid (object). Some exact solutions of this system can be found using methods of the group analysis of differential equations. These solutions could be used to evaluate an error of approximate solutions which obtained by means the linearization of initial (source) system