Experimental Results Related to Discrete Nonlinear Schrödinger Equations
arXiv:0907.4250
Abstract
In this chapter, we discuss experiments that realize the discrete nonlinear Schrödinger (DNLS) equations. The relevance of such descriptions arises from the competition of three common features: nonlinearity, dispersion, and a medium to large level of (periodic, quasiperiodic, or random) discreteness in space. DNLS equations have been especially prevalent in atomic and molecular physics in the study of Bose-Einstein condensates in optical lattices or superlattices; and in nonlinear optics in the description of pulse propagation in waveguide arrays and photorefractive crystals. New experiments in both nonlinear optics and Bose-Einstein condensation provide new challenges for DNLS models, and DNLS and related equations have also recently been used to make important predictions in novel physical settings such as the study of composite metamaterials and arrays of superconducting devices.
17 pages, review article; (document is same as before, but I forgot to include the reference to the published version in Journal-ref); in P. G. Kevrekidis, Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations, and Physics Perspectives, 175-189, Springer Tracts in Modern Physics (Springer-Verlag)