The Resource The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich

The nonlinear Schrödinger equation : singular solutions and optical collapse, Gadi Fibich

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
Creator
Author
Subject
Genre
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. 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 Cergy-Pontoise and Institut des Hautes Études Scientifiques, France
Member of
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
  • Gross-Pitaevskii equations
  • Gross-Pitaevskii 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
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-12748-4
Instantiates
Publication
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 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
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
10.1007/978-3-319-12748-4
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
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-12748-4
Publication
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 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
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
10.1007/978-3-319-12748-4
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

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