Nonlinear Schroedinger Equation

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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• Eletromagnetismo eletricidade, magnetismo e
• Cálculo diferencial e equações
• Física atómica e molecular
• Física óptica

Blowup;Collapse;Dispersive Equations;Nonlinear Optics;Nonlinear Partial Differential Equations;Nonlinear Schrodinger Equation;Nonlinear Waves;Optical Collapse;Self Focusing;Singularity;partial differential equations