Lie Point Symmetries, Traveling Wave Solutions and Conservation Laws of a Non-linear Viscoelastic Wave Equation

This paper studies a non-linear viscoelastic wave equation, with non-linear damping and source terms, from the point of view of the Lie groups theory. Firstly, we apply Lie's symmetries method to the partial differential equation to classify the Lie point symmetries. Afterwards, we reduce the partial differential equation to some ordinary differential equations, by using the symmetries. Therefore, new analytical solutions are found from the ordinary differential equations. Finally, we derive low-order conservation laws, depending on the form of the damping and source terms, and discuss their physical meaning.

Automated summary

This paper investigates a one-dimensional non-linear viscoelastic wave equation with non-linear damping and source terms using Lie group theory. By applying Lie symmetries method, the equation is classified and reduced to ordinary differential equations to find new analytical solutions. Low-order conservation laws are derived based on the form of damping and source terms, with discussions on their physical significance.