arXiv subjects

Almudena del Pilar Márquez

Publications and source records attributed to Almudena del Pilar Márquez.

2 recordsLinked to original sources

arXiv2026

Conservation laws and exact solutions of a nonlinear acoustics equation by classical symmetry reduction

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.

math-ph↗

arXiv2024

Conservation laws for a generalized seventh order KdV equation

In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method in order to classify all point symmetries admitted by the equation in terms of the arbitrary parameters. We find that there are no special cases of the parameters for which the equation admits extra symmetries, other than those that can be found by inspection (scaling symmetry and space and time translation symmetries). We consider the reduced ordinary differential equations and we determined all integrating factors of the reduced equation from the combined $x$- and $t$- translation symmetries. Finally, we observe that all integrating factors arise by reduction of the low-order multipliers of the generalized seventh-order KdV equation.

nlin.SI↗