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Mathematical theory of dispersion-managed optical solitons. (English) Zbl 1201.81002

Nonlinear Physical Science. Berlin: Springer; Beijing: Higher Education Press (ISBN 978-3-642-10219-6/hbk; 978-3-642-10220-2/ebook; 978-7-04-018292-7/hbk). xi, 161 p. (2010).
This is a short text summarizing the analytical and numerical analysis of the propagation of solitons in models of dispersion-management fiber-optic telecommunication links. The dispersion management implies a periodic alternation of fiber segments with negative and positive dispersion, which acts in the combination with the Kerr (cubic) nonlinearity. Multi-channel systems are are described by systems of such equations with the nonlinear (cross-phase-moduolation) coupling terms. The basic mathematical model is the nonlinear Schrödinger (NLS) equation with the dispersion coefficient made a periodic sign-alternating function of the evolutional variable (the propagation distance). The interplay of the periodic “management” with the Kerr nonlinearity gives rise to solitons in the form of robust periodically oscillating pulses, which have a potential for the use in telecommunication networks. The book starts with the introduction to underlying topics, such as the derivation of the NLS equation from the Maxwell’s equations. Then, various aspects of the dynamics of the dispersion-managed (DM) solitons in this model are outlined, in a rather formal manner. Not all relevant aspects of this DM-soliton dynamics are included, and the literature survey is incomplete.

MSC:

81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
35Q51 Soliton equations
49S05 Variational principles of physics
78A60 Lasers, masers, optical bistability, nonlinear optics
81Q37 Quantum dots, waveguides, ratchets, etc.
82D77 Quantum waveguides, quantum wires
94A40 Channel models (including quantum) in information and communication theory
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