A new scheme is presented for fiber transmission of ultrashort laser pulses. A dispersive device divides the input pulses into spatially separated spectral components which are individually launched in the different channels of a multicore fiber before being recombined at the output by a second dispersive device. The parallel transmission of narrow spectral bands avoids self-phase modulation and could be appropriate to deliver high peak power pulses. Phase management of the spectral bands by an active element offers recovery of the seed pulse duration at the fiber output as well as pulse shaping capabilities. Both are reported in a proof of concept experiment using 190 fs input pulses and a 5 cores polarization maintaining fiber. Extension of the concept to femtosecond pulses amplification is suggested.