梁鳳鳴

泰山學(xué)院學(xué)報(bào)編輯部,山東泰安271021

兩個(gè)loop代數(shù)及其應(yīng)用

梁鳳鳴

泰山學(xué)院學(xué)報(bào)編輯部,山東泰安271021

基于兩個(gè)loop代數(shù),利用(2+1)-維零曲率方程分別得到了(2+1)-維超AKNS族和超Tu族.

loop代數(shù);屠格式;(2+1)-維零曲率方程

尋找盡可能多的可積孤立子方程族是孤立子理論研究中的一項(xiàng)重要而有趣的課題,目前流行的方法是屠格式,人們利用屠格式獲得了許多有重要物理意義的可積方程族,如AKNS,KN,BPT族等[1-3];隨著可積系統(tǒng)研究的不斷深入,(2+1)-維可積和超可積系統(tǒng)引起了研究興趣[4-9].在文獻(xiàn)[10]中周子翔教授引入了如下的Lax對(duì)

其相容性條件為

1 (2+1)維超AKNS方程族

在文獻(xiàn)[6]中,馬文秀教授給出了如下的loop代數(shù)B(0,1)

其中E1，E2，E3是偶元,E4,E5是奇元,符號(hào)[,]和[,]分別表示交換子和反交換子.相應(yīng)的loop代數(shù)B~(0,1)為

2 (2+1)維超Tu族

作E1,E2,…,E5的線性組合,則可得如下的loop代數(shù)B1(0,1)

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[4]Zhang Yu-feng,Guo Xiu-rong.A(2+1)-dimensional integrable hierarchy and its extending integrable model[J]. Chaos,Solitons and Fractals,2006,27:555-559

[5]Zhou Zi-xiang.Finite dimensional Hamiltonians andalmaost-periodic solutions for 2+1-dimensional three-wave equations [J].J.Phys.Jpn.,2002,71(8):1857-1863

[6]Ma Wen-xiu,He Jing-song,Qin Zhen-yun.A supertrace identity and its applications to superintegrable systems[J]. Journal of mathematical physics,2008,49:033511

[7]Wang Xin-zeng,Liu Xi-kui.Two types of Lie super-algebra for the super-integrable Tu-hierarchy and its super-Hamiltonian structure[J].Commun.Nonlinear Sci.Numer.Simul.,2010,15:2044-2049

[8]Zhang Yu-feng,Gao Jing.Wang Guang-ming.Two(2+1)-dimensional hierarchies of evolution equations and their Hamiltonian structures[J].Appl.Math.Comput.,2014,243:601-606

[9]Zhang Yu-feng,Rui Wen-juan.On generating(2+1)-dimensional hierarchies of evolution equations[J].Commun Nonlinear Sci.Numer.Simul.2014,19:3454-3461

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Two Super-loop Algebras and Its Application

LIANG Feng-ming
Editorial Department of Journal Taishan University,Taian 271021,China

This paper respectively obtained the(2+1)-dimensional super-AKNS hierarchy and(2+1)-dimensional super-Tu hierarchy with(2+1)-dimensional zero curvature equation based on two super-loop algebras.

Super-loop algebra;Tu scheme;(2+1)-dimensional zero curvature equation

O175.29文獻(xiàn)標(biāo)示碼:A

1000-2324(2015)03-0457-04

2013-07-04

2013-07-24

山東省自然科學(xué)基金項(xiàng)目(ZR2012AL03)

梁鳳鳴(1979-),女,編輯,主要從事期刊編輯研究工作.E-mail:liang-fengming@163.com