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Zbl 1220.35163
Pankov, A.
Gap solitons in periodic discrete nonlinear Schrödinger equations. (English)
[J] Nonlinearity 19, No. 1, 27-40 (2006). ISSN 0951-7715; ISSN 1361-6544/e

Summary: 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.
MSC 2000:
*35Q55 NLS-like (nonlinear Schroedinger) equations
35Q51 Solitons
39A12 Discrete version of topics in analysis
39A70 Difference operators
78A40 Waves and radiation

Cited in: Zbl 1239.39010 Zbl 1193.35176 Zbl 1178.35351 Zbl 1220.35164

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