Initial value problem of the discrete nonlinear Schrödinger equation with complex potential. Issue 16 (2nd November 2022) - Pankov, Alexander; Zhang, Guoping
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.