| 一类非线性演化方程族的可积耦合 |
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| 引用本文： | 张玉峰,许曰才,闫庆友.一类非线性演化方程族的可积耦合[J].高等学校计算数学学报,2005,27(1):46-52. |
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| 作者姓名： | 张玉峰 许曰才 闫庆友 |
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| 作者单位： | 辽宁师范大学数学学院,大连,116029;山东科技大学成人教育学院,泰安,271019;华北电力大学(北京)工商管理学院,北京,102206 |
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| 摘 要： | Starting from a Tu Guizhang‘s isospectral‘problem, a Lax pair is obtained by means of Tu scheme ( we call it Tu Lax pair ). By applying a gauge transformation between matrices, the Tu Lax pair is changed to its equivalent Lax pair with the traces of spectral matrices being zero, whose compatibility gives rise to a type of Tu hierarchy of equations. By making use of a high order loop algebra constructed by us, an integrable coupling system of the Tu hierarchy of equations are presented. Especially, as reduction cases, the integrable couplings of the celebrated AKNS hierarchy, TD hierarchy and Levi hierarchy are given at the same time.
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| 关 键 词： | 可积耦合 非线性演化方程 TD |
INTEGRABLE COUPLINGS OF A TYPE OF NONLINEAR EVOLUTION EQUATIONS |
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| Zhang Yufeng,Xu Yuecai,Yan Qingyou.INTEGRABLE COUPLINGS OF A TYPE OF NONLINEAR EVOLUTION EQUATIONS[J].Numerical Mathematics A Journal of Chinese Universities,2005,27(1):46-52. |
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| Authors: | Zhang Yufeng Xu Yuecai Yan Qingyou |
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| Abstract: | Starting from a Tu Guizhang's isospectral problem, a Lax pair is obtained by means of Tu scheme ( we call it Tu Lax pair ). By applying a gauge transformation between matrices, the Tu Lax pair is changed to its equivalent Lax pair with the traces of spectral matrices being zero, whose compatibility gives rise to a type of Tu hierarchy of equations. By making use of a high order loop algebra constructed by us, an integrable coupling system of the Tu hierarchy of equations are presented. Especially, as reduction cases, the integrable couplings of the celebrated AKNS hierarchy, TD hierarchy and Levi hierarchy are given at the same time. |
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| Keywords: | integrable coupling loop algebra isospectral problem |
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