We study the dynamics of Kerr cavity solitons in the normal dispersion
regime, in the presence of an intracavity phase modulation. The associated
parabolic potential introduces multimode resonances, which promote the
formation of high-order bright solitons. By gradually reducing the potential
strength, bright solitons undergo a transition into dark solitons. We describe
this process as a shift from a multimode resonance to a collapsed snaking
bifurcation structure. This work offers a comprehensive overview of cavity
dynamics and may provide a potential pathway to access multi-stable states by
effectively varying the phase modulation