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arXiv · 2212.06900

Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics

Stephen C. Anco·Almudena P. Marquez·Tamara M. Garrido·Maria L. Gandarias
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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.

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Stephen C. Anco, Almudena P. Marquez, Tamara M. Garrido, Maria L. Gandarias. 2022-12-13. Symmetry analysis and hidden variational structure of Westervelt's equation in nonlinear acoustics. https://doi.org/10.1016/j.cnsns.2023.107315

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