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.