Initial value problem of the discrete nonlinear Schrödinger equation with complex potential. Issue 16 (2nd November 2022)

• Record Type: Journal Article
• Authors: Pankov, Alexander; Zhang, Guoping
• Is Part Of: Applicable analysis. Volume 101:Issue 16(2022)
• Page Start: 5760
• Page End: 5774
• Publication Date: 2022-11-02
• Subjects: Discrete nonlinear Schrödinger equation -- semigroup -- initial value problem -- Lipschitz continuous -- complex potential -- attractor; 37L60 -- 35B41 -- 35Q55; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1906415
• Languages: English
• ISSNs: 0003-6811

Abstract

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.