Nonlinear Super Integrable Couplings of A Super Integrable Hierarchy and Its Super Hamiltonian Structures

TAO Si-xing

doi:10.13371/j.cnki.chin.q.j.m.2018.02.009

Chinese Quarterly Journal of Mathematics >

2018 , Vol. 33 >Issue 2: 181 - 193

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2018.02.009

Nonlinear Super Integrable Couplings of A Super Integrable Hierarchy and Its Super Hamiltonian Structures

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School of Mathematics and Statistics, Shangqiu Normal University

TAO Si-xing(1981-), male, native of Qingzhou, Shandong, an associate professor of Shangqiu Normal University, Ph.D., engages in soliton theory and integrable systems.

Received date: 2016-03-02

Accepted date: 2016-03-02

Online published: 2020-10-09

Supported by

Supported by the Natural Science Foundation of Henan Province(162300410075)； the Science and Technology Key Research Foundation of the Education Department of Henan Province(14A110010)； the Youth Backbone Teacher Foundationof Shangqiu Normal University(2013GGJS02)；

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Abstract

Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.

Key words： Lie super algebra; Nonlinear super integrable couplings; A super integrable hierarchy; Super Hamiltonian structures

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TAO Si-xing . Nonlinear Super Integrable Couplings of A Super Integrable Hierarchy and Its Super Hamiltonian Structures[J]. Chinese Quarterly Journal of Mathematics, 2018 , 33(2) : 181 -193 . DOI: 10.13371/j.cnki.chin.q.j.m.2018.02.009

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