Periodic fixed points of Darboux transformation and decomposition of \((1+1)\)-dimensional integrable systems (Q1309126)

For the Korteweg-de Vries hierarchy of equations the author considers periodic fixed points of Darboux transformations (or appropriate Bäcklund transformations). He proves that the periodic point of an order \(2K + 1\), \(K \in \mathbb{N}\), defines a completely integrable \(K\)- dimensional Hamiltonian system. This work develops the studies by S. Novikov, P. Lax, V. Marchenko, I. Ostrovsky (1974) on a connection between finite- and infinite-dimensional completely integrable Hamiltonian systems and the results by V. Matveev (1984) on Darboux transformations for systems of such a type.