| 矩阵AKNS系列Darboux变换的行列式表示 |
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| 引用本文： | 郑重,贺劲松,程艺.矩阵AKNS系列Darboux变换的行列式表示[J].数学年刊A辑(中文版),2004(1). |
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| 作者姓名： | 郑重 贺劲松 程艺 |
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| 作者单位： | 中国科学技术大学数学系，中国科学技术大学数学系，中国科学技术大学数学系 合肥 230026，合肥 230026，合肥 230026 |
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| 基金项目： | 国家自然科学基金(No.19725104，10101025,10301030)，973项目“非线性科学”资助的项目 |
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| 摘 要： | 本文将建立矩阵AKNS系列Darboux变换的行列式表示。为此,推广了Sylvester恒等式,并利用它化简Darboux迭带所致的行列式 最后,给出了几个著名的矩阵孤立子方程,如矩阵KdV、矩阵NLS、矩阵MKdV等的孤立子解。
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| 关 键 词： | 矩阵AKNS系列 Darboux变换 行列式 孤立子 |
THE DETERMINANT REPRESENTATION OF DARBOUX TRANSFORMS FOR MATRIX AKNS HIERARCHY |
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| ZHENG Zhong HE Jingsong CHENG Yi.THE DETERMINANT REPRESENTATION OF DARBOUX TRANSFORMS FOR MATRIX AKNS HIERARCHY[J].Chinese Annals of Mathematics,2004(1). |
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| Authors: | ZHENG Zhong HE Jingsong CHENG Yi |
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| Institution: | ZHENG Zhong HE Jingsong CHENG Yi
Department of Mathematics,University of Science and Technology of China,Hefei 230026,China. Department of Mathematics,University of Science and Technology of China,Hefei 230026,China.
Department of Mathematics,University of Science and Technology of China,Hefei 230026,China. |
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| Abstract: | The determinant representation of the iterated Darboux Transforms of Matrix AKNS Hierarchy is established. To the purpose, the authors generalize the Sylvester Identity, and use it to simplify the complicated determinants appeared in the process of iterating Darboux transforms. At last, The authors give the soliton solutions of some famous matrix soliton equations such as matrix KdV equation, matrix NLS equation, matrix MKdV equation. |
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| Keywords: | Matrix AKNS Darboux transformation Determinant Soliton |
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