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Zbl 1193.35176
Zhou, Zhan; Yu, Jianshe; Chen, Yuming
On the existence of gap solitons in a periodic discrete nonlinear Schrödinger equation with saturable nonlinearity. (English)
[J] Nonlinearity 23, No. 7, 1727-1740 (2010). ISSN 0951-7715; ISSN 1361-6544/e

Summary: A periodic discrete nonlinear Schrödinger equation with saturable nonlinearity is considered. Using critical point theory in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of gap solitons. Our results not only solve an open problem proposed by {\it A. Pankov} [Nonlinearity 19, No.~1, 27--40 (2006; Zbl 1220.35163)] but also considerably improve some existing ones even for some special cases.

MSC 2000:: *35Q51 Solitons
35Q55 NLS-like (nonlinear Schroedinger) equations
37K40 Soliton theory, asymptotic behavior of solutions
35A35 Theoretical approximation to solutions of PDE
39A12 Discrete version of topics in analysis

Keywords: gap solitons; nonlinear Schrödinger equations

Citations: Zbl 1220.35163

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