An analysis of spatiotemporal localized solutions in the variable coefficients (3 + 1)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters

Under the combined effect of diffraction, anomalous dispersion, and nonlinear refraction, an optical pulse can collapse simultaneously in time and space. Such a collapse could yield short pulses with extremely large optical fields. Light bullets-pulses that propagate without change in space or time-are also possible. The condition for such a collapse and possible experiments are discussed.