11-26【田 凯】腾讯会议 吴文俊数学重点实验室数学物理系列报告之2020-12

发布者:万宏艳发布时间:2020-11-03浏览次数:198

题目: Fermionic extensions of Camassa-Holm and Degasperis-Procesi equations


报告人:田凯,中国矿业大学(北京)



时间:2020年11月26日(星期四)14:00-15:30


地点:腾讯会议 308 482 3910




摘要:Reciprocal transformations are introduced for two super Camassa–Holm (CH) equations, one proposed by Geng et al. [Stud. Appl. Math. 130, 1(2013)] while the other due to Zhang and Zuo [J. Math. Phys. 52, 073503 (2011)]. In the latter case, a new super KdV hierarchy is discovered, and its algebraic properties are established, including Hamiltonian operators, a recursion operator, and conserved quantities. Based on a 4 by 4 matrix spectral problem, a super Degasperis-Procesi (DP) equation is proposed. We show that under a reciprocal transformation the super DP equation is related to a negative flow of a super Kaup-Kupershmidt (KK) hierarchy, which turns out to be a particular reduction of a super Boussinesq hierarchy. With the help of the reciprocal transformation, the bi-Hamiltonian representation of the super DP equation is constructed from that of the super KK hierarchy.