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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

A. Pankov 1,

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

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 and Continuous Dynamical Systems, 2007, 19 (2) : 419-430. doi: 10.3934/dcds.2007.19.419
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