Gap solitons in periodic discrete nonlinear Schrödinger equations

Published 18 October 2005 • 2006 IOP Publishing Ltd and London Mathematical Society
, , Citation A Pankov 2006 Nonlinearity 19 27 DOI 10.1088/0951-7715/19/1/002

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1 Mathematics Department, College of William and Mary, Williamsburg, VA 23187–8795, USA

Dates

  1. Received 31 January 2005
  2. Published

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0951-7715/19/1/27

Abstract

It is shown that the periodic discrete nonlinear Schrödinger equation, with cubic nonlinearity, possesses gap solutions, i.e. standing waves, with the frequency in a spectral gap, that are exponentially localized in the spatial variable. The proof is based on the linking theorem in combination with periodic approximations.

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10.1088/0951-7715/19/1/002