The diversity of experimentally observed nonlinear coherent and partially coherent optical structures, including breathing, zero-dispersion, and switching wave states in driven optical microresonators, is mainly provided by cavity dispersion engineering. Recently, soliton generation was demonstrated on a novel platform - an integrated photonic-crystal Fabry-Perot resonator made of gallium phosphide (GaP) with strongly chirped photonic-crystal mirrors that opened new avenues for arbitrary dispersion engineering [1]. Further attempts to create more broad-band dispersion have led to an oscillatory behavior of the integrated dispersion. Such random dispersion profiles provides a possibility investigate unusual coherent structures and seek promising candidates for such long -standing applied goals as octave-spanning frequency combs.