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Semiclassical Soliton Ensembles For The Focusing Nonlinear Schrödinger Equation

Kamvissis, Spyridon - McLaughlin, Kenneth D T R - Miller, Peter D

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ISBN 10: 0691114838 / ISBN 13: 9780691114835
Verlag: Princeton University Press, 2003
Gebraucht Hardcover
Verkäufer Eastleach Books (Newbury, BER, Vereinigtes Königreich)

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Beschreibung

Laminated boards, F. xiv+265pp, text figs, a fine copy. New. Annals Of Mathematic Studies volume 154. The book offers the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. 600 grams. Buchnummer des Verkäufers 30993

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Bibliografische Details

Titel: Semiclassical Soliton Ensembles For The ...

Verlag: Princeton University Press

Erscheinungsdatum: 2003

Einband: Hardcover

Auflage: 1st edition..

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Inhaltsangabe:


This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe.


To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis.


About the Author:

Spyridon Kamvissis is a researcher at the Max Planck Institute of Mathematics in Bonn, Germany, and a Professor of Mathematics at the National Technical University in Athens, Greece. Kenneth D. T-R McLaughlin is Associate Professor of Mathematics at the University of North Carolina, Chapel Hill. Peter D. Miller is Assistant Professor of Mathematics at the University of Michigan, Ann Arbor.

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