The linearity of the power response of yttrium iron garnet films to a microwave pulse having length shorter than the delay time characteristic of the specimen is investigated. In particular, a threshold is found above which output power increases with respect to standard linear trend. The above novel effect, analyzed in some detail on five epilayers of different thicknesses, cannot be explained in terms of usual nonlinear processes. An interpretation in terms of soliton excitation, accounting for the existence in the system of both intrinsic nonlinearity and dispersion, is proposed. PACS numbers: 75.30.Ds, 76.50.+g, 85.70.Ge Presently, solitons are an active field of interest in both fundamental and applied solid-state physics. The mathematical advances in finding out analytical solutions to a certain number of nonlinear dispersive wave functions 1 have given a powerful tool to their study and characterization.As is well established, a soliton results as a fairly delicate balance between the dispersion (which forces the signal to spread out) and the nonlinearity (which forces the signal to steepen) of the system under investigation. Apart from the interest in basic research, the remarkable applications of soliton propagation in optical fibers, 2 nonlinear transmission lines, 3 and Josephson junctions 4 (just to mention a few of them) seem to justify the search for solitons in media which are inherently both dispersive and nonlinear. Some systems in the field of acoustical 5 and radio-frequency signal transmission are in principle suitable to fit those requirements. Among them, the analysis of possible soliton excitation in a magnetostatic wave (MSW) device such as a dispersive delay line 6 operating at microwave frequency is particularly appealing. From a theoretical standpoint, a dipolar model dealing with the nonlinear properties of nonexchange MSW's propagating in a low-loss magnetic film of yttrium iron garnet (YIG) has been recently developed. 7 To account only for nonlinearities produced by self-action processes, a nonlinear Schrodinger equation describing the evolution of envelope solitons has been derived in the weak nonlinearity approximation. In this way, expected threshold powers for the onset of selfmodulation and self-channeling have been derived.Furthermore, through an analysis of the unique experimental data available in current literature, it turns out that attempts to detect purely magnetostatic solitons in YIG films have been so far unsuccessful. 8 In this framework, some nonlinear phenomena, interpreted in terms of multisoliton excitation as deduced by our analyzing the time envelope of an output pulsed signal, 8,9 have been reported. In order to get that result, the operational frequency had to fall within a few defined regions of the spectrum close to so-called repulsion gaps. 10 According to the theory and experimental findings, 11 resolvable gaps can be observed under specific conditions of spin pinning whenever the dipolar and exchange energy terms are comparable in magnitude. From an ...