%0 Journal Article 
%A Anco, Stephen C.
%A Recio Rodríguez, Elena
%T Topological charges and conservation laws involving an arbitrary function of time for dynamical PDEs
%D 2021
%@ 1471-2946
%U http://hdl.handle.net/10498/33275
%X Dynamical PDEs that have a spatial divergence
form possess conservation laws that involve an
arbitrary function of time. In one spatial dimension,
such conservation laws are shown to describe the
presence of an x-independent source/sink; in two
and more spatial dimensions, they are shown to
produce a topological charge. Two applications are
demonstrated. First, a topological charge gives rise
to an associated spatial potential system, allowing
non-local conservation laws and symmetries to be
found for a given dynamical PDE. This type of
potential system has a different form and different
gauge freedom compared to potential systems that
arise from ordinary conservation laws. Second, when
a topological charge arises from a conservation law
whose conserved density is non-trivial off of solutions
to the dynamical PDE, then this relation yields a
constraint on initial/boundary data for which the
dynamical PDE will be well posed. Several examples
of nonlinear PDEs from applied mathematics and
integrable system theory are used to illustrate these
results.
%K mathematical physics
%K differential equations
%~ Universidad de Cádiz