Continuous symmetries in spatially extended systems
Spatially extended systems are infinite dimensional dynamical
systems which are constructed by defining a nonlinear partial
differential equation, such as
Navier-Stokes equations, under periodic boundary conditions.
Such representation of nonlinear PDEs enables us to apply the
methods of the nonlinear dynamics to their study. In my research,
I focus on understanding the symmetries of these systems and
developing symmetry-invairant representation methods.