The Nonlinear Schrödinger Equation Singular Solutions and Optical Collapse /

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 s...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Fibich, Gadi (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:Applied Mathematical Sciences, 192
Temas:
Differential equations.
Atoms.
Molecules.
Electrodynamics.
Nonlinear Optics.
Differential Equations.
Atomic, Molecular and Chemical Physics.
Classical Electrodynamics.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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