Communications in Mathematical Analysis

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

Sergiy Bak and Galyna Kovtonyuk

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Abstract

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

Source
Commun. Math. Anal., Volume 22, Number 2 (2019), 18-34.

Dates
First available in Project Euclid: 4 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.cma/1575428421

Mathematical Reviews number (MathSciNet)
MR4033734

Zentralblatt MATH identifier
07161349

Subjects
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

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

Citation

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


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