Electron. J. Differential Equations, Vol. 2016 (2016), No. 287, pp. 1-14.

Gap solitons in periodic Schrödinger lattice system with nonlinear hopping

Ming Cheng, Alexander Pankov

This article concerns the periodic discrete Schrödinger equation with nonlinear hopping on the infinite integer lattice. We obtain the existence of gap solitons by the linking theorem and concentration compactness method together with a periodic approximation technique. In addition, the behavior of such solutions is studied as $\alpha\to 0$. Notice that the nonlinear hopping can be sign changing.

Submitted October 7, 2016. Published October 26, 2016.
Math Subject Classifications: 35Q55, 35Q51, 39A12, 39A70, 78A40.
Key Words: Discrete nonlinear Schrödinger equation; nonlinear hopping; gap soliton; linking theorem; periodic approximation.

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Ming Cheng
College of Mathematics
Jilin University
Changchun 130012, China
email: jlumcheng@hotmail.com
Alexander Pankov
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: alexander.pankov@morgan.edu

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