Communications in Mathematical Analysis
- Commun. Math. Anal.
- Volume 22, Number 2 (2019), 18-34.
Existence of Standing Waves in DNLS with Saturable Nonlinearity on 2D-Lattice
In this paper we obtain results on existence of standing waves in Discrete Nonlinear Shrödinger equation (DNLS) with saturable nonlinearity on a two-dimensional lattice. We consider two types of solutions: with periodic amplitude and vanishing at infinity (localized solution). Sufficient conditions for the existence of such solutions are obtained with the aid of Nehari manifold and periodic approximations.
Commun. Math. Anal., Volume 22, Number 2 (2019), 18-34.
First available in Project Euclid: 4 December 2019
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35Q51: Soliton-like equations [See also 37K40] 39A12: Discrete version of topics in analysis 39A70: Difference operators [See also 47B39] 35A15: Variational methods
Bak, Sergiy; Kovtonyuk, Galyna. Existence of Standing Waves in DNLS with Saturable Nonlinearity on 2D-Lattice. Commun. Math. Anal. 22 (2019), no. 2, 18--34. https://projecteuclid.org/euclid.cma/1575428421