Initial value problem of the discrete nonlinear Schrödinger equation with complex potential

Abstract

In this paper we study the time-dependent discrete nonlinear Schrödinger equation with complex, not necessarily bounded, potential and sufficiently general nonlinearity on a multi dimensional lattice. Under natural assumptions we prove the global well-posedness in weighted $l^2$ spaces. In the dissipative case we obtain a result on the existence of global compact attractor in such spaces.

Keywords:

• Discrete nonlinear Schrödinger equation
• semigroup
• initial value problem
• Lipschitz continuous
• complex potential
• attractor

2010 Mathematics Subject Classifications:

• 37L60
• 35B41
• 35Q55

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Simons Foundation [410289].