We report the generation of self-frequency-shifting Raman quasisolitons in a pulse-pumped high-$Q$ fiber Fabry-Perot resonator in the weak normal dispersion regime. They are induced by modulation instability mediated by fourth-order dispersion in a regime where the Raman gain overwhelms the cavity losses. The resulting spectrum, spanning over 50 THz, is reminiscent of the supercontinuum generated in single-pass waveguides. We clearly identify this process using a dispersive Fourier transform experiment. Additionally, we demonstrate the suppression of modulation instability by tuning the synchronization mismatch between the pump repetition rate and the cavity round-trip time, enabling the generation of a standard dissipative Kerr soliton in this system. These observations align remarkably well with numerical simulations based on a generalized Lugiato-Lefever equation, incorporating the Raman response of the optical fiber.

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• Nonlinear optics
• Stimulated Raman scattering
• Solitons