2004/01/08 by Andrei K. Svinin, A. K. Svinin, Svinin, A. K.
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0401008
Latex, 22 p., accepted for publication in Theor. Math. Phys
openalex publication_date 2004/01/08 · arxiv created 2004/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Invariant submanifolds of the so-called Darboux-KP chain are investigated. It is shown that restriction of dynamics on some class of invariant submanifolds yields the extension of the discrete KP hierarchy, while the intersections leads to Lax pairs for a broad class of differential-difference systems with finite number of fields. Some attention is given to investigation of self-similar reductions. It is shown that self-similar ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. Some examples are provided. In particular it is shown that well known first discrete Painleve equation (dPI) corresponds to Volterra lattice hierarchy. It is written down equations which naturally generalize dPI in the sense that they have first Painleve transcedent in continuous limit.