Abstract
We analyze spatio-temporal pulse propagation in graded-index Kerr materials with the variational method, and find that if the path of propagation provides negative group-velocity dispersion, stable solitary pulses exist for pulse energy smaller than a critical value. Spatial and temporal degrees of freedom cannot be analyzed separately due to their coupling through the Kerr nonlinarity. Our unified analysis not only elucidates the hidden coupling, but also clarifies relations between parameters of the solitary pulse. The analysis is verified by direct numerical simulation of the paraxial wave equation.
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