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

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  • Additional Information
    • Contributors:
      Matemáticas
    • Publication Information:
      Preprint
    • Publication Information:
      Elsevier BV, 2023.
    • Publication Date:
      2023
    • 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.
      23 pages; published version
    • File Description:
      application/pdf
    • ISSN:
      1007-5704
    • Accession Number:
      10.1016/j.cnsns.2023.107315
    • Accession Number:
      10.48550/arxiv.2212.06900
    • Rights:
      CC BY NC ND
      CC BY
    • Accession Number:
      edsair.doi.dedup.....6767435d107c9788712bb38f1a35153d