兩個loop代數及其應用

梁鳳鳴

泰山學院學報編輯部,山東泰安271021

兩個loop代數及其應用

梁鳳鳴

泰山學院學報編輯部,山東泰安271021

基于兩個loop代數,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;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];隨著可積系統研究的不斷深入,(2+1)-維可積和超可積系統引起了研究興趣[4-9].在文獻[10]中周子翔教授引入了如下的Lax對

其相容性條件為

1 (2+1)維超AKNS方程族

在文獻[6]中,馬文秀教授給出了如下的loop代數B(0,1)

其中E1，E2，E3是偶元,E4,E5是奇元,符號[,]和[,]分別表示交換子和反交換子.相應的loop代數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B1(0,1)

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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文獻標示碼:A

1000-2324(2015)03-0457-04

2013-07-04

2013-07-24

山東省自然科學基金項目(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