Variational analysis of spatio-temporal pulse dynamics in dispersive Kerr media

The spatio-temporal dynamics of pulse propagation in dispersive Kerr media is studied based on the variational principle. By performing a Ritz optimization procedure with spatio-temporal Gaussian test functions, the equations of motion for the pulse parameters are derived. Comparison of these analytical results with numerically obtained solutions of the exact problem show very good agreement over a broad range of dispersion, diffraction, and nonlinearity parameters. (C) 2002 Optical Society of America.