- 08-83 Dirk Hundertmark, Young-Ran Lee
- Super-exponential decay of Diffraction Managed Solitons
Apr 23, 08
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Abstract. 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 Schr\"odinger equation. In this part we study the diffraction managed discrete non-linear Schr\"odinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management
geometries. We show that, for vanishing average diffraction, all solutions of the non-linear and non-local diffraction management equation decay super-exponentially.
As a byproduct of our method, we also have a simple proof of existence of diffraction managed solitons in the case of vanishing average diffraction.