We consider the dynamics of a coherent seed undergoing a free electron laser high gain amplification. We discuss the dispersion of the optical packet during the interaction and study the problem using different formalisms, including that of the Wigner distribution. The analysis we develop is mainly based on a 1D procedure; the inclusion of transverse longitudinal interplay is also briefly discussed. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.