Communications in Mathematical Analysis

Existence of Standing Waves in DNLS with Saturable Nonlinearity on 2D-Lattice

Sergiy Bak and Galyna Kovtonyuk

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

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

discrete nonlinear Schrodinger equation 2D-lattice standing waves critical points Nehari manifold saturable nonlinearity periodic approximations


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.

Export citation