The Nonlinear Schrödinger Equation Singular Solutions and Optical Collapse /

• Κύριος συγγραφέας: Fibich, Gadi (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Σειρά: Applied Mathematical Sciences, 192
• Θέματα: Mathematics.; Partial differential equations.; Optics.; Electrodynamics.; Atoms.; Physics.; Statistical physics.; Partial Differential Equations.; Atomic, Molecular, Optical and Plasma Physics.; Optics and Electrodynamics.; Nonlinear Dynamics.

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 su...

Πίνακας περιεχομένων:

• 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.