RT journal article
T1 Conservation laws and exact solutions of a nonlinear acoustics equation by classical symmetry reduction
A1 Márquez Lozano, Almudena del Pilar
A1 Recio Rodríguez, Elena
A1 Gandarias Núñez, María Luz
A2 Matemáticas
K1 Nonlinear acoustics
K1 Symmetries
K1 Conservation laws
K1 Conserved quantities
K1 Travelling waves
K1 Shock waves
AB 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.
PB Elsevier Ltd
SN 0960-0779
YR 2025
FD 2025-02-01
LK http://hdl.handle.net/10498/38253
UL http://hdl.handle.net/10498/38253
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-nov-2026