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

Almudena P. Márquez and María S. Bruzón
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Almudena P. Márquez: Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain
María S. Bruzón: Department of Mathematics, University of Cadiz, Puerto Real, 11510 Cadiz, Spain

Mathematics, 2021, vol. 9, issue 17, 1-11

Abstract: 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.

Keywords: viscoelastic wave equation; Lie symmetries; traveling wave solutions; conversation laws (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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