Ground states for the higher-order dispersion managed NLS equation in the absence of average dispersion

Markus Kunze; Jamison Moeser; Vadim Zharnitsky

doi:10.1016/j.jde.2004.09.014

Ground states for the higher-order dispersion managed NLS equation in the absence of average dispersion

Markus Kunze, Jamison Moeser, Vadim Zharnitsky

Research output: Contribution to journal › Article › peer-review

Abstract

The problem of existence of ground states in higher-order dispersion managed NLS equation is considered. The ground states are stationary solutions to dispersive equations with nonlocal nonlinearity which arise as averaging approximations in the context of strong dispersion management in optical communications. The main result of this note states that the averaged equation possesses ground state solutions in the practically and conceptually important case of the vanishing residual dispersions.

Original language	English (US)
Pages (from-to)	77-100
Number of pages	24
Journal	Journal of Differential Equations
Volume	209
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2004.09.014
State	Published - Feb 1 2005

Keywords

Dispersion management
Ground states
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

Online availability

10.1016/j.jde.2004.09.014

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title = "Ground states for the higher-order dispersion managed NLS equation in the absence of average dispersion",

abstract = "The problem of existence of ground states in higher-order dispersion managed NLS equation is considered. The ground states are stationary solutions to dispersive equations with nonlocal nonlinearity which arise as averaging approximations in the context of strong dispersion management in optical communications. The main result of this note states that the averaged equation possesses ground state solutions in the practically and conceptually important case of the vanishing residual dispersions.",

keywords = "Dispersion management, Ground states, Nonlinear Schr{\"o}dinger equation",

author = "Markus Kunze and Jamison Moeser and Vadim Zharnitsky",

note = "Funding Information: Part of this research was carried out while V. Zharnitsky was visiting Program in Applied and Computational Mathematics at Princeton University. He would like to thank Ingrid Daubechies for her hospitality and for providi ng stimulating research environment. V. Zharnitsky was supported by NSF und er grant No. DMS-0219233. J.M. gratefully acknowledges the support of NSF Grant DMS-9810751.",

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AU - Kunze, Markus

AU - Moeser, Jamison

AU - Zharnitsky, Vadim

N1 - Funding Information: Part of this research was carried out while V. Zharnitsky was visiting Program in Applied and Computational Mathematics at Princeton University. He would like to thank Ingrid Daubechies for her hospitality and for providi ng stimulating research environment. V. Zharnitsky was supported by NSF und er grant No. DMS-0219233. J.M. gratefully acknowledges the support of NSF Grant DMS-9810751.

PY - 2005/2/1

Y1 - 2005/2/1

N2 - The problem of existence of ground states in higher-order dispersion managed NLS equation is considered. The ground states are stationary solutions to dispersive equations with nonlocal nonlinearity which arise as averaging approximations in the context of strong dispersion management in optical communications. The main result of this note states that the averaged equation possesses ground state solutions in the practically and conceptually important case of the vanishing residual dispersions.

AB - The problem of existence of ground states in higher-order dispersion managed NLS equation is considered. The ground states are stationary solutions to dispersive equations with nonlocal nonlinearity which arise as averaging approximations in the context of strong dispersion management in optical communications. The main result of this note states that the averaged equation possesses ground state solutions in the practically and conceptually important case of the vanishing residual dispersions.

KW - Dispersion management

KW - Ground states

KW - Nonlinear Schrödinger equation

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Ground states for the higher-order dispersion managed NLS equation in the absence of average dispersion

Abstract

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