RT journal article
T1 Symmetry analysis and hidden variational structure of Westervelt’s equation in nonlinear acoustics
A1 Anco, Stephen C.
A1 Márquez Lozano, Almudena del Pilar
A1 Garrido Letrán, Tamara María
A1 Gandarias Núñez, María Luz
A2 Matemáticas
K1 Conservation laws
K1 Conserved integrals
K1 Nonlinear acoustics
K1 Symmetries
AB 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 the general dissipative version of Westervelt's 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; hidden variational structures, including a Lagrangian and a Hamiltonian; a recursion operator and a Noether operator; contact symmetries; higher-order symmetries and higher-order conservation laws.
PB Elsevier
SN 1007-5704
YR 2023
FD 2023-05-20
LK http://hdl.handle.net/10498/28939
UL http://hdl.handle.net/10498/28939
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026