RT journal article
T1 Topological charges and conservation laws involving an arbitrary function of time for dynamical PDEs
A1 Anco, Stephen C.
A1 Recio Rodríguez, Elena
A2 Matemáticas
K1 mathematical physics
K1 differential equations
AB Dynamical PDEs that have a spatial divergenceform possess conservation laws that involve anarbitrary function of time. In one spatial dimension,such conservation laws are shown to describe thepresence of an x-independent source/sink; in twoand more spatial dimensions, they are shown toproduce a topological charge. Two applications aredemonstrated. First, a topological charge gives riseto an associated spatial potential system, allowingnon-local conservation laws and symmetries to befound for a given dynamical PDE. This type ofpotential system has a different form and differentgauge freedom compared to potential systems thatarise from ordinary conservation laws. Second, whena topological charge arises from a conservation lawwhose conserved density is non-trivial off of solutionsto the dynamical PDE, then this relation yields aconstraint on initial/boundary data for which thedynamical PDE will be well posed. Several examplesof nonlinear PDEs from applied mathematics andintegrable system theory are used to illustrate theseresults.
PB The Royal Society Publishing
SN 1471-2946
YR 2021
FD 2021
LK http://hdl.handle.net/10498/33275
UL http://hdl.handle.net/10498/33275
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026