We investigated the properties of pulse propagation on nonlinear traveling-wave field effect transistors (TW-FET) to develop a method for amplifying short electrical pulses. TW-FETs are a special type of FET whose electrodes are employed not only as electrical contacts but also as transmission lines. Due to the presence of electromagnetic couplings between the gate and drain lines, two different propagation modes called the c mode and π mode are developed on a TW-FET. Moreover, the Schottky contact beneath the gate electrode creates an ideal source of nonlinearity for soliton-like propagation. We can design the TW-FET to amplify only soliton-like pulses carried by one of the two modes and attenuate the ones carried by the other mode. This paper discusses the fundamental properties of a nonlinear TW-FET, including the width and velocity of a soliton-like pulse carried by c and π modes, and gives design criteria of amplification of soliton-like pulses.