We perform calculations of the nuclear modification factors $R_{AA}$ and $I_{AA}$ for collisions of light nuclei at the LHC energies for scenarios with and without quark-gluon plasma formation in pp collisions. We find a sizeable difference in $R_{AA}$ and $I_{AA}$ for these two scenarios, which grows with decreasing atomic number. This says that data on the nuclear modification factors for light nuclei could give information on the presence of jet quenching in pp collisions. Preliminary data from the CMS Collaboration on O+O and Ne+Ne collisions obtained in 2025 support the scenario with quark-gluon plasma formation in pp collisions.

Classical works, dedicated to the finite-gap intrgration, admits the following interpretation. One has g finite circles on the spectral curve, and each oval contains exactly one zero of the wave function. A set of g circles is exactly the g-dimensional torus, which is exactly the Liouville torus. The Abel transform linearizes the motion of this tours. If one consideres degenerate curves, corresponding to the multisoliton solutions, the defintion of divisors requires a refinement, including the resolution of singularities. We show that for the so-called MM-curves and Dubrovin-Natanzon divisors, generating real regular multisoliton KP-2 solutions, it is sufficient to apply only the two simplest types of resolutions.

Recently, a big number of papers dedicated to the study of PT-symmetric operators and integrable equations has been published. In the finite-gaps approach to the 1-d Schrodinger operators two alternative approaches can be used: 1) Matvees-Its approach based on the theory of Riemann theta-functions; 2) Dubrovin's approach based on the divisor's dynamics. The characterization of PT-symmetric Schrodinger operators in the first approach was recentky obtained by Taimanov. In our parer we describe the spectral curves and divisor trajectories for such operators in the first-order approximation.

Through a massive computation we reached the fourth superharmonic instability branch of the Stokes' wave. Using the obtained results we checked phenomenological formulae for the dependence of the instability growth rates corresponding to different branches of instability on the nonlinearity parameter (steepness, defined as the wave swing to wavelength ratio) in the vicinity of the new instability branch appearance and far from it. It is demonstrated, that the formulae, the one obtained as a least squares fit using the information from the first three branches of instability and a phenomenological asymptotics, work for the fourth branch and previously reported branches as well. Range of applicability of the relations was corrected. Growth rates for all four instability branches are reported.