超HU方程族的自相容源及其守恒律

doi:10.3969/j.issn.1000-5641.2019.02.003

华东师范大学学报(自然科学版) ›› 2019, Vol. 2019 ›› Issue (2): 21-31.doi: 10.3969/j.issn.1000-5641.2019.02.003

超HU方程族的自相容源及其守恒律

方芳, 胡贝贝

滁州学院数学与金融学院, 安徽滁州 239000

收稿日期:2017-12-24 出版日期:2019-03-25 发布日期:2019-03-27
通讯作者: 胡贝贝,男,博士研究生,讲师,研究方向为孤立子与可积系统.E-mail:hubsquare@chzu.edu.cn E-mail:hubsquare@chzu.edu.cn
作者简介:方芳,女,讲师,研究方向为孤立子与可积系统.E-mail:fangfang7679@163.com.
基金资助:
国家自然科学基金（11601055）；安徽省自然科学研究项目（KJ2015B02）；安徽省教育厅自然科学一般项目（KJ2017B10）

Conservation laws and self-consistent sources for a super-HU equation hierarchy

FANG Fang, HU Bei-bei

School of Mathematics and Finance, Chuzhou University, Chuzhou Anhui 239000, China

Received:2017-12-24 Online:2019-03-25 Published:2019-03-27

摘要/Abstract

摘要： 基于超矩阵李代数和超迹恒等式，建立了超HU方程族.然后又构造了超HU方程族的带有自相容源方程.最后通过引入两个变量F和G，获得了超HU方程族的无穷多个守恒律.

关键词: 超HU方程族, 自相容源, 守恒律

Abstract: In the present paper, a super-HU hierarchy was constructed based on super-matrix Lie algebra and super-trace identity. In addition, an integrable super-HU equation hierarchy with self-consistent sources was established. Finally, we set up infinitely many conservation laws for an integrable super-HU equation hierarchy by introducing two variables F and G.

Key words: super-HU hierarchy, self-consistent sources, conservation laws

中图分类号:

O175.29

方芳, 胡贝贝. 超HU方程族的自相容源及其守恒律[J]. 华东师范大学学报(自然科学版), 2019, 2019(2): 21-31.

FANG Fang, HU Bei-bei. Conservation laws and self-consistent sources for a super-HU equation hierarchy[J]. Journal of East China Normal University(Natural Sc, 2019, 2019(2): 21-31.

参考文献

[1] HU X B. A powerful approach to generate new integrable systems[J]. Journal of Physics A:Mathematical and General, 1994, 27:2497-2514.
[2] HU X B. An approach to generate superextensions of integrable systems[J]. Journal of Physics A:Mathematical and General, 1997, 30:619-632.
[3] MA W X, HE J S, QIN Z Y. A supertrace identity and its applications to superintegrable systems[J]. Journal of Mathematics Physics, 2008, 49:033511.
[4] WEI H Y, XIA T C. Nonlinear integrable couplings of super Kaup-Newell hierarchy and its super Hamiltonian structures[J]. Acta Physica Sinica, 2013, 62:13-20.
[5] TAO S X, XIA T C. Nonlinear super-integrable couplings of super Broer-Kaup-Kupershmidt Hierarchy and its super Hamiltonian structures[J]. Advances in Mathematica Physics, 2013:520765.
[6] DONG H H, WANG X Z. Lie algebras and Lie super algebra for the integrable couplings of NLS-MKdV hierarchy[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14:4071-4077.
[7] MEL'NIKOV V K. Intersection of the nonlinear schrodinger equation with a source[J]. Inverse Problems, 1992, 8:133-147.
[8] DOKTROV E V, VLASOV R A. Optical solitons in media with combined resonant and non-resonant (cubic) nonlinearities in the presence of perturbations[J]. Journal of Optics, 1991, 38:31-45.
[9] MEL'NIKOV V K. Integration of the Korteweg-de Vries equation with a source[J]. Inverse Problems, 1990, 6:233-246.
[10] ZAKHAROV V E, KUZNETSOV E A. Multi-scale expansitions in the theory of systems integrable by the inverse scattering transform[J]. Physica D:Nonlinear phenomena, 1986, 18:455-463.
[11] MEL'NIKOV V K. Integration of method of the Korteweg-de Vries equation with a self-consistent source[J]. Physics Letters A, 1988, 133:493-496.
[12] LEON J. Solution of an initial-boundary value problem for coupled nonlinear waves[J]. Journal of Physics A:Mathematics and General, 1990, 23:1385-1403.
[13] LEON J. Spectral transform and solitons for generalized coupled Bloch systems[J]. Journal of Mathematical Physics, 1988, 29:2012-2019.
[14] 胡贝贝, 张玲, 方芳. Li谱问题的超化及其自相容源[J]. 吉林大学学报(理学版), 2015, 53:229-234.
[15] ZHANG D J. The N-soliton solutions of the MKdV equation with self-consistent sources[J]. Chaos, Solitons and Fractals, 2003, 18:31-43.
[16] ZENG Y B, MA W X, SHAO Y J. Two binary Darboux transformations for the KdV hierarchy with self-consistent sources[J]. Journal of Mathematical Physics, 2001, 42:2113-2128.
[17] ZENG Y B, SHAO Y J, MA W X. Integral-type darboux transformations for the mKdV hierarchy with selfconsistent sources[J]. Communications in theoretical Physics, 2002, 38:641-648.
[18] LI L. Conservation laws and self-consistent sources for a super-CKdV equation hierarchy[J]. Physics Lett A, 2011, 375:1402-1406.
[19] WANG H, XIA T C. Conservation laws for a super G-J hierarchy with self-consistent sources[J]. Communications in Nonlinear Science and Numerical Simulation, 2012, 17:566-572.
[20] MIURA R M, GARDNER C S, KRUSKAL M D. Korteweg-de Vries equation and generalizations Ⅱ:Existence of conservation laws and constants of motion[J]. Journal of Mathematical Physics, 1968, 9:1204-1209.
[21] 胡贝贝, 张玲. 超经典Boussinesq系统的守恒律和自相容源[J]. 数学杂志, 2016, 36:584-590.
[22] WANG H, XIA T C. Conservation laws and self-consistent sources for a super KN hierarchy[J]. Appl Math Comput, 2013, 219:5458-5464.
[23] LI L. Conservation laws and self-consistent sources for a super-CKdV equation hierarchy[J]. Physics Letters A, 2011, 375:1402-1406.
[24] TAO S X. Self-Consistent sources and conservation laws for super coupled Burgers equation hierarchy[J]. International Journal of Applied Physics and Mathematics, 2013, 3:252-256.
[25] TU G Z. An extension of a theorem on gradients of conserved densities of integrable system[J]. Northeastern Math J, 1990, 6:26-32.
[26] ZHAI Y Y, GENG X G. Straightening out of the flows for the Hu hierarchy and its algebro-geometric solutions[J]. Math Anal Appl J, 2013, 397(2):561-576.

超HU方程族的自相容源及其守恒律

Conservation laws and self-consistent sources for a super-HU equation hierarchy

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