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

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May 2007, 19(2): 419-430. doi: 10.3934/dcds.2007.19.419

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

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

Received May 2005 Revised July 2005 Published July 2007

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

Mathematics Subject Classification: 35Q55, 35Q51, 39A12, 39A70, 78A4.

Citation: A. Pankov. Gap solitons in periodic discrete nonlinear Schrödinger equations II: A generalized Nehari manifold approach. Discrete & Continuous Dynamical Systems - A, 2007, 19 (2) : 419-430. doi: 10.3934/dcds.2007.19.419

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