Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics
Abstract
Westervelt's equation is a nonlinear wave equation that is widely used to model the propagation of sound waves in a compressible medium, with one important application being ultra-sound in human tissue. Two fundamental aspects of this equation -- symmetries and conservation laws -- are studied in the present work by modern methods. Numerous results are obtained: new conserved integrals; potential systems yielding hidden symmetries and nonlocal conservation laws; mapping of Westervelt's equation in the undamped case into a linear wave equation; exact solutions arising from the mapping; hidden variational structures, including a Lagrangian and a Hamiltonian; a recursion operator and a Noether operator; contact symmetries; higher-order symmetries and conservation laws.
Keywords
Cite
@article{arxiv.2212.06900,
title = {Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics},
author = {Stephen C. Anco and Almudena P. Marquez and Tamara M. Garrido and Maria L. Gandarias},
journal= {arXiv preprint arXiv:2212.06900},
year = {2023}
}
Comments
23 pages; published version