The Whitham Equations for Optical Communications: Mathematical Theory of NRZ
Author:
- Yuji KodamaYKYuji Kodama
- 1 January 1999
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 59 (6) , 2162-2192
Abstract
We present a model of optical communication system for high-bit-rate data transmission in the nonreturn-to-zero (NRZ) format over transoceanic distance. The system operates in a small group velocity dispersion regime, and the model equation is given by the well-known Whitham equations describing the slow modulation of multiphase wavetrains of the (defocusing) nonlinear Schrödinger (NLS) equation. The model equation is of hyperbolic type, and NRZ pulse with certain initial phase modulation develops a shock. We then show how one can obtain a global solution by choosing an appropriate Riemann surface on which the Whitham equation is defined. We also discuss the effect of third order dispersion by using an integrable hierarchy of the NLS equation, and we give a condition to avoid a shock formation.Keywords
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This publication has 23 references indexed in Scilit:
- The semiclassical limit of the defocusing NLS hierarchyCommunications on Pure and Applied Mathematics, 1999
- Onset of Oscillations in Nonsoliton Pulses in Nonlinear Dispersive FibersJournal of Nonlinear Science, 1998
- Recent Progress in Dispersion-Managed Soliton Transmission TechnologiesOptical Fiber Technology, 1997
- Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchyCommunications in Mathematical Physics, 1996
- Bit-synchronous polarisation and phase modulationscheme for improving theperformance of optical amplifier transmission systemsElectronics Letters, 1996
- Decay of an initial discontinuity in the defocusing NLS hydrodynamicsPhysica D: Nonlinear Phenomena, 1995
- Dispersive Regularization of the Whitham Equation for the Toda LatticeSIAM Journal on Applied Mathematics, 1992
- Korteweg-de Vries equation with finite-gap boundary conditions, and the Whitham deformations of Riemann surfacesFunctional Analysis and Its Applications, 1989
- Optical solitons in a monomode fiberJournal of Statistical Physics, 1985
- Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equationCommunications on Pure and Applied Mathematics, 1980