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- Title
Conservation laws and variational structure of damped nonlinear wave equations.
- Authors
Anco, Stephen C.; Márquez, Almudena P.; Garrido, Tamara M.; Gandarias, Maria L.
- Abstract
All low‐order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time‐dependent. Such equations arise in numerous physical applications and have attracted much attention in analysis. The conservation laws describe generalized momentum and boost momentum, conformal momentum, generalized energy, dilational energy, and light cone energies. Both the conformal momentum and dilational energy have no counterparts for nonlinear undamped wave equations in one dimension. All of the conservation laws are obtainable through Noether's theorem, which is applicable because the damping term can be transformed into a time‐dependent self‐interaction term by a change of dependent variable. For several of the conservation laws, the corresponding variational symmetries have a novel form which is different than any of the well‐known variational symmetries admitted by nonlinear undamped wave equations in one dimension.
- Subjects
CONSERVATION laws (Physics); NONLINEAR wave equations; CONSERVATION laws (Mathematics); NOETHER'S theorem; LIGHT cones
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 6, p3974
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9798