We demonstrate that ultrashort optical pulses propagating in a nonlinear dispersive medium are naturally described through\r\nincorporation of analytic signal for the electric field. To this end a second-order nonlinear wave equation is first simplified using a\r\nunidirectional approximation. Then the analytic signal is introduced, and all nonresonant nonlinear terms are eliminated. The\r\nderived propagation equation accounts for arbitrary dispersion, resonant four-wave mixing processes, weak absorption, and\r\narbitrary pulse duration. The model applies to the complex electric field and is independent of the slowly varying envelope\r\napproximation. Still the derived propagation equation posses universal structure of the generalized nonlinear Schr�¨odinger equation\r\n(NSE). In particular, it can be solved numerically with only small changes of the standard split-step solver or more complicated\r\nspectral algorithms for NSE.We present exemplary numerical solutions describing supercontinuum generation with an ultrashort\r\noptical pulse.
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