TY - JOUR
T1 - Factorization Problems on Rational Loop Groups, and the Poisson Geometry of Yang-Baxter Maps
AU - Li, Luen Chau
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2022/3
Y1 - 2022/3
N2 - The study of set-theoretic solutions of the Yang-Baxter equation, also known as Yang-Baxter maps, is historically a meeting ground for various areas of mathematics and mathematical physics. In this work, we study factorization problems on rational loop groups, which give rise to Yang-Baxter maps on various geometrical objects. We also study the symplectic and Poisson geometry of these Yang-Baxter maps, which we show to be integrable maps in the sense of having natural collections of Poisson commuting integrals. In a special case, the factorization problems we consider are associated with the N-soliton collision process in the n-Manakov system, and in this context we show that the polarization scattering map is a symplectomorphism.
AB - The study of set-theoretic solutions of the Yang-Baxter equation, also known as Yang-Baxter maps, is historically a meeting ground for various areas of mathematics and mathematical physics. In this work, we study factorization problems on rational loop groups, which give rise to Yang-Baxter maps on various geometrical objects. We also study the symplectic and Poisson geometry of these Yang-Baxter maps, which we show to be integrable maps in the sense of having natural collections of Poisson commuting integrals. In a special case, the factorization problems we consider are associated with the N-soliton collision process in the n-Manakov system, and in this context we show that the polarization scattering map is a symplectomorphism.
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U2 - 10.1007/s11040-022-09419-4
DO - 10.1007/s11040-022-09419-4
M3 - Article
AN - SCOPUS:85125319220
SN - 1385-0172
VL - 25
JO - Mathematical Physics Analysis and Geometry
JF - Mathematical Physics Analysis and Geometry
IS - 1
M1 - 6
ER -