H. Huh, S. Hussain, and D.E. Pelinovsky
Chern-Simons-Schrodinger theory on a one-dimensional lattice
Letters in Mathematical Physics 110 (2020) 2221-2244
Abstract:
We propose a gauge-invariant system of the Chern-Simons-Schrodinger type
on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global
well-posedness of the initial-value problem in the space of square summable sequences for
the scalar field. We also study the existence region of the stationary bound states, which
depends on the lattice spacing and the nonlinearity power. A major difficulty in the existence
problem is related to the lack of variational formulation of the stationary equations. Our
approach is based on the implicit function theorem in the anti-continuum limit and the
solvability constraint in the continuum limit.
Keywords:
Chern-Simons-Schrodinger equations, initial-value problem, discrete solitons, continuum limit, anti-continuum limit