For the most part in this volume, we have analyzed solitary wave coherent structures that constitute the prototypical nonlinear wave solutions of the ubiquitous discrete nonlinear Schr–dinger (DNLS) model. A natural question, however, that arises is how do these structures emerge from general initial data. One possible answer to that question stems from the modulational instability mechanism that we addressed in some detail in both focusing and defocusing DNLS equations in Chap. 6. Another possibility that we will address in this section is the formation of such nonlinear excitations from localized initial data. In fact, the latter approach was experimentally pioneered in [1], where an injected beam of light was introduced into one waveguide of a waveguide array. It was observed that when the beam had low intensity, then it dispersed through quasi-linear propagation.
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Kevrekidis, P.G. (2009). Formation of Localized Modes in DNLS. 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_12
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