数聚西海岸科学讲堂2024年第17期:Jingping Wang教授学术报告

发布时间:2024-04-23 阅读量:

报告题目:Hamiltonian, preHamiltonian and Nijenhuis rational difference operators

报告人: Jingping Wang

工作单位: University of Kent, UK




We introduce preHamiltonian pairs of difference operators and study their connections with Nijenhuis and Hamiltonian operators.
A difference operator is called preHamiltonian if its image is a Lie subalgebra with respect to the Lie bracket of evolutionary vector fields on a difference field. Two preHamiltonian operators form a preHamiltonian pair if any their linear combination is preHamiltonian. Then we show that preHamiltonian pairs naturally lead to Nijenhuis operators. Moreover, Nijenhuis operators can be represented in terms of a preHamiltonian pair. This provides a systematic method to check whether a rational operator is Nijenhuis.
We explore the link between preHamiltonian and Hamiltonian operators and show show that if H is a rational Hamiltonian operator, then to find a second Hamiltonian operator K compatible with H is the same as to find a preHamiltonian pair A and B such that K=AB^{-1}H is skew-symmetric.
In the end, we illustrate our theory on known and new examples. This is the joint work with S. Carpentier and A.V. Mikhailov.


Jingping Wang, 本科毕业于北京大学,博士毕业于荷兰鹿特丹大学, 现为英国肯特大学教授、博士生导师, 主要从事可积系统理论的研究工作, 在Commun. Math. Phys., Lett. Math. Phys.等期刊上发表多篇高质量SCI论文。