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应用数学学报  2013, Vol. 36 Issue (6): 1000-1007    DOI:
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几类新的(2+1)维具有无穷维Virasoro型对称代数的可积方程组
王丽真1, 黄晴1, 沈守枫2, 高雯1,3
1. 西北大学数学系, 非线性科学研究中心, 西安 710069;
2. 浙江工业大学数学系, 杭州 310014;
3. 西北农林科技大学理学院, 杨陵 712100
Some New (2+1)-Dimensional Integrable Systems with Infinitely Dimensional Virasoro-type Symmetry Algebra
WANG Lizhen1, HUANG Qing1, SHEN Shoufeng2, Gao Wen1,3
1. Center for Nonlinear Studies, Department of Mathematics, Northwest University, Xi'an 710069;
2. Department of Mathematics, Zhejiang University of Technology, Hangzhou 310014;
3. College of Science, Northwest A & F University, Yanglin 712100
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摘要 寻找和构造高维可积模型是非线性可积系统的重要课题之一. 在楼森岳和胡星标提出的关于Virasoro型可积理论的指导下,利用无穷维无中心的Virasoro型对称子代数和向量场的延拓结构理论,已经得到了许多高维可积方程. 把该方法推广到方程组上,通过选取特殊的实现,本文构造了几类具有无穷维Virasoro对称子代数意义下的可积方程组并且所得到的方程组与一类特殊的广义(2+1)维MKdV(Modified Korteweg-de Vries)方程组同构.
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王丽真
黄晴
沈守枫
高雯
关键词Virasoro型代数   Virasoro型可积方程组   (2+1)维MKdV方程组   非线性可积系统     
Abstract: Seeking and constructing high dimensional integrable models is one of the important subjects in nonlinear integrable system. Under the instruction of the theory proposed by Lou and Hu, applying infinitely dimensional centerless Virasoro type symmetry algebra and prolongation theory of the vector fields, many new high dimensional integrable equations have been obtained. Generalize this method to system, by means of choosing special realization, in this study, some (2+1)-dimensional Virasoro integrable systems in the meaning of possessing infinite dimensional Virasoro type symmetry algebra are constructed. In addition, the systems we derived are isomorphic to the special case of the (2+1)-dimensional MKdV(Modified Korteweg-de Vries) system.
Key wordsVirasoro type algebra   Virasoro integrable system   (2+1)-dimensional MKdV system   nonlinear integrable system   
收稿日期: 2013-07-25;
基金资助:国家自然科学基金(11201371,11001240,11101332),陕西省自然科学基础研究计划基金(2012JQ1013) 及陕西省教育厅科研基金(11JK0482)资助项目.
引用本文:   
王丽真,黄晴,沈守枫等. 几类新的(2+1)维具有无穷维Virasoro型对称代数的可积方程组[J]. 应用数学学报, 2013, 36(6): 1000-1007.
WANG Lizhen,HUANG Qing,SHEN Shoufeng et al. Some New (2+1)-Dimensional Integrable Systems with Infinitely Dimensional Virasoro-type Symmetry Algebra[J]. Acta Mathematicae Applicatae Sinica, 2013, 36(6): 1000-1007.
 
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