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The nonlinear Schrodinger equationsi...

Fibich, Gadi.

The nonlinear Schrodinger equationsingular solutions and optical collapse /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The nonlinear Schrodinger equationby Gadi Fibich.
Reminder of title:	singular solutions and optical collapse /
Author:	Fibich, Gadi.
Published:	Cham :Springer International Publishing :2015.
Description:	xxxi, 862 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Gross-Pitaevskii equations.
Online resource:	http://dx.doi.org/10.1007/978-3-319-12748-4
ISBN:	9783319127484 (electronic bk.)

The nonlinear Schrodinger equationsingular solutions and optical collapse /
Fibich, Gadi.

The nonlinear Schrodinger equationsingular solutions and optical collapse /[electronic resource] :by Gadi Fibich. - Cham :Springer International Publishing :2015. - xxxi, 862 p. :ill. (some col.), digital ;24 cm. - Applied mathematical sciences,v.1920066-5452 ;. - Applied mathematical sciences ;v.176..

Derivation of the NLS -- Linear propagation -- Early self-focusing research -- NLS models -- Existence of NLS solutions -- Solitary waves -- Variance identity -- Symmetries and the lens transformation -- Stability of solitary waves -- The explicit critical singular peak-type solution -- The explicit critical singular ring-type solution -- The explicit supercritical singular peak-type solution -- Blowup rate, blowup profile, and power concentration -- The peak-type blowup profile -- Vortex solutions -- NLS on a bounded domain -- Derivation of reduced equations -- Loglog law and adiabatic collapse -- Singular H1 ring-type solutions -- Singular H1 vortex solutions -- Singular H1 peak-type solutions -- Singular standing-ring solutions -- Singular shrinking-ring solutions -- Critical and threshold powers for collapse -- Multiple filamentation -- Nonlinear Geometrical Optics (NGO) method -- Location of singularity -- Computation of solitary waves -- Numerical methods for the NLS -- Effects of spatial discretization -- Modulation theory -- Cubic-quintic and saturated nonlinearities -- Linear and nonlinear damping -- Nonparaxiality and backscattering (nonlinear Helmholtz equation) -- Ultrashort pulses -- Normal and anomalous dispersion -- NGO method for ultrashort pulses with anomalous dispersion -- Continuations beyond the singularity -- Loss of phase and chaotic interactions.

This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrodinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrodinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. "This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics) It will be extremely useful for students and researchers who enter this field." Frank Merle, Universite de Cergy-Pontoise and Institut des Hautes Etudes Scientifiques, France

ISBN: 9783319127484 (electronic bk.)

Standard No.: 10.1007/978-3-319-12748-4doiSubjects--Topical Terms:

715984
Gross-Pitaevskii equations.

LC Class. No.: QC174.26.W28

Dewey Class. No.: 530.124

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245 1 4 $a The nonlinear Schrodinger equation $h [electronic resource] : $b singular solutions and optical collapse / $c by Gadi Fibich.
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490 1 $a Applied mathematical sciences, $x 0066-5452 ; $v v.192
505 0 $a Derivation of the NLS -- Linear propagation -- Early self-focusing research -- NLS models -- Existence of NLS solutions -- Solitary waves -- Variance identity -- Symmetries and the lens transformation -- Stability of solitary waves -- The explicit critical singular peak-type solution -- The explicit critical singular ring-type solution -- The explicit supercritical singular peak-type solution -- Blowup rate, blowup profile, and power concentration -- The peak-type blowup profile -- Vortex solutions -- NLS on a bounded domain -- Derivation of reduced equations -- Loglog law and adiabatic collapse -- Singular H1 ring-type solutions -- Singular H1 vortex solutions -- Singular H1 peak-type solutions -- Singular standing-ring solutions -- Singular shrinking-ring solutions -- Critical and threshold powers for collapse -- Multiple filamentation -- Nonlinear Geometrical Optics (NGO) method -- Location of singularity -- Computation of solitary waves -- Numerical methods for the NLS -- Effects of spatial discretization -- Modulation theory -- Cubic-quintic and saturated nonlinearities -- Linear and nonlinear damping -- Nonparaxiality and backscattering (nonlinear Helmholtz equation) -- Ultrashort pulses -- Normal and anomalous dispersion -- NGO method for ultrashort pulses with anomalous dispersion -- Continuations beyond the singularity -- Loss of phase and chaotic interactions.
520 $a This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrodinger equation. With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. It combines rigorous analysis, asymptotic analysis, informal arguments, numerical simulations, physical modelling, and physical experiments. It repeatedly emphasizes the relations between these approaches, and the intuition behind the results. The Nonlinear Schrodinger Equation will be useful to graduate students and researchers in applied mathematics who are interested in singular solutions of partial differential equations, nonlinear optics and nonlinear waves, and to graduate students and researchers in physics and engineering who are interested in nonlinear optics and Bose-Einstein condensates. It can be used for courses on partial differential equations, nonlinear waves, and nonlinear optics. Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University. "This book provides a clear presentation of the nonlinear Schrodinger equation and its applications from various perspectives (rigorous analysis, informal analysis, and physics) It will be extremely useful for students and researchers who enter this field." Frank Merle, Universite de Cergy-Pontoise and Institut des Hautes Etudes Scientifiques, France
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