2025/12/21 by V. E. Adler, Adler, V. E., V. I. Sokolov +1
Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · doi:10.48550/arxiv.2512.18828
The group reduction procedure is applied to vector generalizations of the NLS, mKdV, and KdV equations. The resulting ODE systems admit isomonodromic Lax representations and are multicomponent generalizations of the Painlevé equations P1, P2, P34, and P4. Some of them can be interpreted as nonautonomous deformations of well-known systems integrable in the Liouville sense, in particular, the Garnier and Hénon--Heiles systems. In one case, an unexpected connection with the equations of quasiperiodic dressing chain for the Schrödinger operator is established.