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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 16
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Research Article

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

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Pages 5760-5774 | Received 09 Jul 2020, Accepted 04 Mar 2021, Published online: 26 Apr 2021
 

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 l2 spaces. In the dissipative case we obtain a result on the existence of global compact attractor in such spaces.

2010 Mathematics Subject Classifications:

Disclosure statement

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

Additional information

Funding

This work was supported by Simons Foundation [410289].

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