Discrete nonlinear Schrödinger (DNLS) equations can be used to model numerous phenomena in atomic, molecular, and optical physics. The general feature of these various settings that leads to the relevance of DNLS models is a competition between nonlinearity, dispersion, and spatial discreteness (which can be periodic, quasiperiodic, or random).
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Acknowledgements
I would like to thank Panos Kevrekidis for the invitation to write this article. I would also like to acknowledge Martin Centurion, Panos Kevrekidis, Alex Nicolin, Yaron Silberberg, and Ian Spielman for reading and providing critical comments on drafts of this manuscript. Finally, I also thank Markus Oberthaler, Moti Segev, and Yaron Silberberg for permission to use their figures.
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Porter, M.A. (2009). Experimental Results Related to DNLS Equations. In: The Discrete Nonlinear Schrödinger Equation. Springer Tracts in Modern Physics, vol 232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89199-4_8
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