Gap solitons in periodic discrete nonlinear Schrödinger equations II: A generalized Nehari manifold approach

A. Pankov

doi:10.3934/dcds.2007.19.419

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2007, Volume 19, Issue 2: 419-430. Doi: 10.3934/dcds.2007.19.419

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Gap solitons in periodic discrete nonlinear Schrödinger equations II: A generalized Nehari manifold approach

A. Pankov^1,

1.
Mathematics Department, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795

Received: April 30, 2005

Revised: June 30, 2005

Published: April 2007

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Abstract

In the present article we obtain the existence of so-called ground gap solitons in discrete periodic nonlinear Schrödinger equations with cubic nonlinearity. To do that we employ a periodic approximation technique and a generalized Nehari manifold approach.

Keywords:

Gap solitons,
discrete nonlinear Schrödinger equation,
ground states,
Nehari manifold.

Mathematics Subject Classification: 35Q55, 35Q51, 39A12, 39A70, 78A40.

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Gap solitons in periodic discrete nonlinear Schrödinger equations II: A generalized Nehari manifold approach

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