Heat and thermal travelling wave solutions of a nonlinear Maxwell-Cattaneo-Vernotte equation

TL;DR

This paper investigates heat and thermal wave propagation using a nonlinear Maxwell-Cattaneo-Vernotte equation, deriving exact solutions that reveal conditions for soliton formation and illustrating these with plots.

Contribution

It introduces a novel approach by expressing thermal conductivity and relaxation time as polynomial functions of temperature to find exact wave solutions.

Findings

Identified polynomial degrees leading to soliton solutions

Derived exact wave solutions for nonlinear thermal equations

Provided illustrative plots for specific parameter values

Abstract

The propagation of heat and thermal signals in the form of travelling waves is investigated for a nonlinear Maxwell-Cattaneo-Vernotte equation. The exact wave solutions are derived by expressing the thermal conductivity and the relaxation time as polynomial functions of the temperature. This approach enables the identification of suitable degrees of nonlinearity that give rise to soliton solutions. Finally, exact solutions are shown through plots for the values of the selected parameters.