Study of Soliton Stabilization in D+1 Dimensions using Novel Analytical and Numerical Techniques

In this Chapter, we provide a brief review of the underlying nonlinear Schrödinger and associated equations that model spatio-temporal propagation in one and higher dimensions in a nonlinear dispersive environment. Particular attention is given to fast adaptive numerical techniques to solve such equations, and in the presence of dispersion and nonlinearity management, saturating nonlinearity and nonparaxiality. A unique variational approach is also outlined which helps in determining the ranges of nonlinearity and dispersion parameters to ensure stable solutions of the nonlinear equations. The propagation of 3+1 dimensional spatio-temporal pulses, or optical bullets is also modeled using a fast adaptive split-step Hankel transform technique