Global well-posedness for discrete non-linear Schrödinger equation

Abstract

We consider the initial value problem for the discrete non-linear Schrödinger equation in weighted l ²-spaces. Under quite general assumptions we prove that the problem is globally well-posed. The proof is based on simple general facts on abstract evolution equations.

Keywords:

• global well-posedness
• discrete Schrödinger equation
• mild solution
• semigroups of operators

AMS Subject Classifications::

• 35Q55
• 35A05