Yang-Baxter maps and matrix solitons. (English) Zbl 1061.35091

Goncharenko, V. M.; Veselov, A. P.

Shabat, A.B.(ed.) et al., New trends in integrability and partial solvability. Proceedings of the NATO Advanced Research Workshop, Cadiz, Spain, June 12–16, 2002. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1835-5/hbk). NATO Science Series II: Mathematics, Physics and Chemistry 132, 191-197 (2004).

Summary: New examples of the Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) on the Grassmannians, arising from the theory of the matrix Korteweg-de Vries equation are discussed. The Lax pairs for these maps are produced using the relations with the inverse scattering problem for the matrix Schrödinger operator.
For the entire collection see [Zbl 1050.35003].

MSC:

35Q40	PDEs in connection with quantum mechanics
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Keywords:

matrix factorization; Grassmannian; Lax pairs; quantum Yang-Baxter equation