The optical response of axially uniform nonlinear photonic bandgap fibers is studied theoretically. We observe gap-soliton-like generation and associated bistability, similar to what is typically found in periodically modulated nonlinear structures. This response stems from the nature of the guided-mode dispersion relations, which involve a frequency cutoff at zero wave vector. In such systems, solutions with zero group velocities and minimal coupling to radiation modes come in naturally. We term such solitons "cutoff solitons"; they provide an interesting alternative to gap solitons in periodically index-modulated fibers for in-fiber all-optical signal processing.