
11.3. MODULATION INSTABILITY
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Indeed, these two approaches are applicable when the dimensionless parameter ah is
either small or large. In the intermediate case, one must rely on the numerical solu-
tions with the exact dispersion relations (11.2.12). However, it is useful to consider
a simplified model that can describe, at least qualitatively, the situation close to the
Bragg-reflection gap (fl _~ ill) and is valid for ah _~ 1. To achieve this goal, we extend
the tight-binding approximation and the corresponding discrete NLS equation to this
new regime.
Equation (11.2.16) can be considered a rough discretization of the original ...