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The Resource The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich
The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich
Resource Information
The item The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blowup) solutions of the nonlinear Schrödinger 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 Schrödinger 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 BoseEinstein 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. 2This 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. 3 Frank Merle, Université de CergyPontoise and Institut des Hautes Études Scientifiques, France
 Language
 eng
 Extent
 1 online resource (xxxi, 862 pages)
 Contents

 Derivation of the NLS
 Linear propagation
 Early selffocusing research
 NLS models
 Existence of NLS solutions
 Solitary waves
 Variance identity
 Symmetries and the lens transformation
 Stability of solitary waves
 The explicit critical singular peaktype solution
 The explicit critical singular ringtype solution
 The explicit supercritical singular peaktype solution
 Blowup rate, blowup profile, and power concentration
 The peaktype blowup profile
 Vortex solutions
 NLS on a bounded domain
 Derivation of reduced equations
 Loglog law and adiabatic collapse
 Singular H1 ringtype solutions
 Singular H1 vortex solutions
 Singular H1 peaktype solutions
 Singular standingring solutions
 Singular shrinkingring 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
 Cubicquintic 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
 Isbn
 9783319127477
 Label
 The nonlinear Schrödinger equation : singular solutions and optical collapse
 Title
 The nonlinear Schrödinger equation
 Title remainder
 singular solutions and optical collapse
 Statement of responsibility
 Gadi Fibich
 Subject

 Calculus
 Mathematics
 Science  Molecular Physics
 Electronic books
 GrossPitaevskii equations
 Nonlinear Dynamics
 Atomic, Molecular, Optical and Plasma Physics
 Atomic & molecular physics
 Differential calculus & equations
 Physical Sciences & Mathematics
 GrossPitaevskii equations
 Science  Electricity
 Science  Chaotic Behavior in Systems
 Partial Differential Equations
 Optical physics
 Mathematics  Differential Equations
 Mathematics
 Nonlinear science
 Optics and Electrodynamics
 Language
 eng
 Summary
 This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blowup) solutions of the nonlinear Schrödinger 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 Schrödinger 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 BoseEinstein 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. 2This 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. 3 Frank Merle, Université de CergyPontoise and Institut des Hautes Études Scientifiques, France
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Fibich, Gadi
 Dewey number
 530.12/4
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QC174.26.W28
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Applied mathematical sciences,
 Series volume
 volume 192
 http://library.link/vocab/subjectName

 GrossPitaevskii equations
 GrossPitaevskii equations
 Mathematics
 Physical Sciences & Mathematics
 Calculus
 Mathematics
 Partial Differential Equations
 Atomic, Molecular, Optical and Plasma Physics
 Optics and Electrodynamics
 Nonlinear Dynamics
 Science
 Science
 Science
 Atomic & molecular physics
 Optical physics
 Nonlinear science
 Mathematics
 Differential calculus & equations
 Label
 The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Derivation of the NLS  Linear propagation  Early selffocusing research  NLS models  Existence of NLS solutions  Solitary waves  Variance identity  Symmetries and the lens transformation  Stability of solitary waves  The explicit critical singular peaktype solution  The explicit critical singular ringtype solution  The explicit supercritical singular peaktype solution  Blowup rate, blowup profile, and power concentration  The peaktype blowup profile  Vortex solutions  NLS on a bounded domain  Derivation of reduced equations  Loglog law and adiabatic collapse  Singular H1 ringtype solutions  Singular H1 vortex solutions  Singular H1 peaktype solutions  Singular standingring solutions  Singular shrinkingring 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  Cubicquintic 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
 Dimensions
 unknown
 Extent
 1 online resource (xxxi, 862 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319127477
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9783319127484
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)904797130
 (OCoLC)ocn904797130
 Label
 The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Derivation of the NLS  Linear propagation  Early selffocusing research  NLS models  Existence of NLS solutions  Solitary waves  Variance identity  Symmetries and the lens transformation  Stability of solitary waves  The explicit critical singular peaktype solution  The explicit critical singular ringtype solution  The explicit supercritical singular peaktype solution  Blowup rate, blowup profile, and power concentration  The peaktype blowup profile  Vortex solutions  NLS on a bounded domain  Derivation of reduced equations  Loglog law and adiabatic collapse  Singular H1 ringtype solutions  Singular H1 vortex solutions  Singular H1 peaktype solutions  Singular standingring solutions  Singular shrinkingring 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  Cubicquintic 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
 Dimensions
 unknown
 Extent
 1 online resource (xxxi, 862 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319127477
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Note
 SpringerLink
 Other control number
 10.1007/9783319127484
 Other physical details
 illustrations (some color).
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)904797130
 (OCoLC)ocn904797130
Subject
 Atomic & molecular physics
 Atomic, Molecular, Optical and Plasma Physics
 Calculus
 Differential calculus & equations
 Electronic books
 GrossPitaevskii equations
 GrossPitaevskii equations
 Mathematics
 Mathematics
 Mathematics  Differential Equations
 Nonlinear Dynamics
 Nonlinear science
 Optical physics
 Optics and Electrodynamics
 Partial Differential Equations
 Physical Sciences & Mathematics
 Science  Chaotic Behavior in Systems
 Science  Electricity
 Science  Molecular Physics
Genre
Member of
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