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By using a reductive perturbation method, we derive from Maxwell-Blochequations a cubic generalized Kadomtsev-Petviashvili equation for ultrashortspatiotemporal optical pulse propagation in cubic (Kerr-like) media without theuse of the slowly varying envelope approximation. We calculate the collapsethreshold for the propagation of few-cycle spatiotemporal pulses described bythe generic cubic generalized Kadomtsev-Petviashvili equation by a directnumerical method and compare it to analytic results based on a rigorous virialtheorem. Besides, typical evolution of the spectrum (integrated over thetransverse spatial coordinate) is given and a strongly asymmetric spectralbroadening of ultrashort spatiotemporal pulses during collapse is evidenced.

Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation