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Zbl 1197.35273
Pankov, Alexander
Gap solitons in periodic discrete nonlinear Schrödinger equations with saturable nonlinearities. (English)
[J] J. Math. Anal. Appl. 371, No. 1, 254-265 (2010). ISSN 0022-247X

Summary: The main result of the paper concerns the existence of nontrivial exponentially decaying solutions to periodic stationary discrete nonlinear Schrödinger equations with saturable nonlinearities, provided that zero belongs to a spectral gap of the linear part. The proof is based on the critical point theory in combination with periodic approximations of solutions. As a preliminary step, we prove also the existence of nontrivial periodic solutions with arbitrarily large periods.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
39A12 Discrete version of topics in analysis
35C08
81Q05 Closed and approximate solutions to quantum-mechanical equations
35A15 Variational methods (PDE)
35B10 Periodic solutions of PDE

Keywords: discrete nonlinear Schrödinger equation; gap soliton; periodic approximation; linking theorem

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