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The Resource The Nonlinear Schrödinger Equation : Singular Solutions and Optical Collapse, by Gadi Fibich, (electronic resource)

The Nonlinear Schrödinger Equation : Singular Solutions and Optical Collapse, by Gadi Fibich, (electronic resource)

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
by Gadi Fibich
Creator
Contributor
Author
Subject
Language
eng
Summary
This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) 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 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. zThis 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.y Frank Merle, Université de Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Member of
http://library.link/vocab/creatorName
Fibich, Gadi
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Applied Mathematical Sciences,
Series volume
192
http://library.link/vocab/subjectName
  • Mathematics
  • Partial differential equations
  • Optics
  • Electrodynamics
  • Atoms
  • Physics
  • Statistical physics
Label
The Nonlinear Schrödinger Equation : Singular Solutions and Optical Collapse, by Gadi Fibich, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-12748-4
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-3-319-12748-4
Dimensions
unknown
Extent
XXXI, 862 p. 202 illus., 100 illus. in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319127484
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-12748-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086504879
Label
The Nonlinear Schrödinger Equation : Singular Solutions and Optical Collapse, by Gadi Fibich, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-319-12748-4
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-3-319-12748-4
Dimensions
unknown
Extent
XXXI, 862 p. 202 illus., 100 illus. in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319127484
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-12748-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086504879

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