 Conservation laws and exact solutions of a nonlinear acoustics equation by classical symmetry reductionAlmudena P. Márquez, Elena Recio and María L. Gandarias Chaos, Solitons & Fractals, 2025, vol. 191, issue C Abstract: Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely used in nonlinear acoustics and it is especially important in biomedical applications such as ultra-sound imaging in human tissue. Modern methods are applied to uncover point symmetries and conservation laws that can lead to useful developments concerning solutions and their properties. A complete classification of point symmetries is shown for the arbitrary function. Local low-order conservation laws related to net mass of sound waves are obtained by the multiplier method. Two potential systems are derived yielding potential symmetries and nonlocal conservation laws. For the physical case interesting for this equation, travelling wave solutions are studied leading to shock waves. Keywords: Nonlinear acoustics; Symmetries; Conservation laws; Conserved quantities; Travelling waves; Shock waves (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014772 DOI: 10.1016/j.chaos.2024.115925 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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