An accurate wave equation beyond the slowly varying envelope approximation for femtosecond soliton propagation in an optical fiber is derived by the iterative method.The derived equation contains higher nonlinear terms than the generalized nonlinear Schrodinger equation obtained previously. For a silica-based fiber, we have shown that the higher nonlinear terms in the derived equation are negligible for optical pulses in the single cycle regime. The propagations of a 5 fs fundamental soliton and 10 fs and 50 fs second-order solitons in an optical fiber are numerically simulated. We have found that when a fs fundamental soliton propagates in a fiber, it becomes asymmetric ith an oscillatory structure nhear its trailing edge and the main pulse broadens. We have also found that, for the 10 fs second-order soliton, the soliton decay is dominated by the third-order dispersion, and for the 50 fs second-order soliton, the soliton decay is dominated by the delayed Raman response.
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