On the Eigenvalues of the Manakov System

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Date
2007-06-26
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Virginia Tech
Abstract

We clear up two issues regarding the eigenvalue problem for the Manakov system; these problems relate directly to the existence of the soliton [sic] effect in fiber optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, then it must lie in a certain region in the complex plane. The second issue has to do with a chirped Manakov system. We show that if a system is chirped too much, the soliton effect disappears. While this has been known for some time experimentally, there has not yet been a theoretical result along these lines for the Manakov system.

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Keywords
Zakharov-Shabat, chirp, fiber optics, inverse scattering transform, soliton, coupled nonlinear Schrödinger equations, nonlinear Schrödinger equation, Manakov
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