2008/04/23 by Dirk Hundertmark, Hundertmark, Dirk, Young-Ran Lee +1
Physics and Astronomy · #Nonlinear Photonic Systems #Advanced Fiber Laser Technologies #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0804.3783
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 Schrödinger equation. In this part we study the diffraction managed discrete non-linear Schrödinger 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.