Download e-book for iPad: Optical Solitons: Theoretical Challenges and Industrial by A. Hasegawa (auth.), V. E. Zakharov, S. Wabnitz (eds.)

By A. Hasegawa (auth.), V. E. Zakharov, S. Wabnitz (eds.)

ISBN-10: 3540663142

ISBN-13: 9783540663140

ISBN-10: 3662038072

ISBN-13: 9783662038079

This e-book offers an outline of modern theoretical and experimental advances within the box of optical solitons, starting from the mathematical foundations of integrability conception to the swiftly evolving know-how of fiber soliton-based telecommunication platforms. the topics coated within the publication might be commonly grouped into 4 major different types: optical soliton concept, fiber soliton telecommunications, optical soliton iteration equipment, and all-optical details processing through spatial solitons. This publication should still supply an enticing reference either for postgraduate scholars beginning their study within the box, and researchers actively inquisitive about nonlinear optics and optical communications.

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Extra resources for Optical Solitons: Theoretical Challenges and Industrial Perspectives: Les Houches Workshop, September 28 – October 2, 1998

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Adler, "Legendre transformations ... " solv-int/9R08016, [8] R. Hirota J. Phys. Soc. Japan, 43, 2074-78 (1977); ibid 50, p 3785-91, (1981). I. Yamilov, Usp. Mat. Nauk, 38, No 6, 155-15(), (198:3). B. Suris, Phys. Lett. A, 145, ll3-ll9 (1990). P. A. Dynnikov, Usp. Mat. )-234, (1997). N. B. I. Yamilov, Phys. Lett. A, 174, 397, (1993). A. D. , 117334 Moscow, Russia 1. INTRODUCTION The main aim of this article is to demonstrate two methods for investigating the stability of solitons. We restrict ourselves to consideration of two basic models, namely, the nonlinear Schrodinger equation (NLSE) and the three-wave system.

2 -- 0. The latter, as one can check out, generates the stereographic projection of unit sphere Sr + S5 + 8g = 1 onto plane u, v. l) yields a generic example of polynomial hamiltonian density (8) which admits the first order parametrizations of momentum (10) (Cf [4],[5)). Parametrizations of momentum of the zero and the first orders yield distinct normal forms (7) of one and the same dynamical system (1). ) (13) which is more simple in comparison with the first order case with F, G of a general form (7).

25) can be performed. fJ'I/Jl' with a familiar change in all integrals of motion. 27) instead of dl it is necessary to substitute the matrix inverse to w~fJ, the velocities vl there have meaning of vectors. These changes allow us to restrict our consideration to the one-dimensional 3-wave system only. Of course, there exists some difference between onedimensional and multi-dimensional cases but it is not too fundamental for this system, at least as far as soliton stability concerns. 17) corresponds to the stationary wave propagation, when in the equations the time derivative is equal to zero.

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Optical Solitons: Theoretical Challenges and Industrial Perspectives: Les Houches Workshop, September 28 – October 2, 1998 by A. Hasegawa (auth.), V. E. Zakharov, S. Wabnitz (eds.)


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