  Some afterglow light curves of gamma-ray bursts (GRBs) exhibit very complex
temporal and spectral features, such as a sudden intensity jump about one hour
after the prompt emission in the optical band. We assume that this feature is
due to the late collision of two relativistic shells and investigate the
corresponding high-energy neutrino emission within a multi-messenger framework,
while contrasting our findings with the ones from the classic afterglow model.
For a constant density circumburst medium, the total number of emitted
neutrinos can increase by about an order of magnitude when an optical jump
occurs with respect to the self-similar afterglow scenario. By exploring the
detection prospects with the IceCube Neutrino Observatory and future radio
arrays such as IceCube-Gen2 radio, RNO-G and GRAND200k, as well as the POEMMA
spacecraft, we conclude that the detection of neutrinos with IceCube-Gen2 radio
could enable us to constrain the fraction of GRB afterglows with a jump as well
as the properties of the circumburst medium. We also investigate the neutrino
signal expected for the afterglows of GRB 100621A and a GRB 130427A-like burst
with an optical jump. The detection of neutrinos from GRB afterglows could be
crucial to explore the yet-to-be unveiled mechanism powering the optical jumps.
