Super-Exponential Decay of Diffraction Managed Solitons

초록

This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schrodinger equation. In this part we study the diffraction managed discrete non-linear Schrodinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management geometries. We show that, for vanishing average diffraction, any solution f is an element of l(2)(Z) of the non-linear and non-local diffraction management equation decays super-exponentially. More precisely, we have the bound lim sup (|x|) (->) (infinity) ((|x| + 1)ln(|x| + 1)(-1) ln |f(x)| <= -1/4 for any diffraction management soliton.

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