| 一族新的Lax可积格方程和它的积耦合体系 |
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| 引用本文： | 夏铁成,赵文英,张娇.一族新的Lax可积格方程和它的积耦合体系[J].渤海大学学报(自然科学版),2006,27(1):21-24. |
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| 作者姓名： | 夏铁成 赵文英 张娇 |
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| 作者单位： | 1. 上海大学,数学系,上海,200436
2. 渤海大学,数学系,辽宁,锦州,121013 |
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| 摘 要： | 首先利用环代数^~A1和微分算子构建一种新的代数系统X。其次，利用这种代数系统提出了一个新的等谱问题，由离散的零曲率方程得到Lax可积的立方Volterra格方程族。最后，通过扩展代数系统X得出了立方Volterra格方程族的可积耦合体系。这种方法也能被应用到其它的格方程族中。
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| 关 键 词： | 代数系统 立方Volterra格方程族 可积耦合系统 |
| 文章编号： | 1673-0569(2006)01-0021-04 |
| 收稿时间： | 05 15 2005 12:00AM |
| 修稿时间： | 2005年5月15日 |
A new hierarchy of Lax integrable lattice equations and its integrable couplings system |
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| XIA Tie-cheng,ZHAO Wen-ying,ZHANG Jiao.A new hierarchy of Lax integrable lattice equations and its integrable couplings system[J].Journal of Bohai University:Natural Science Edition,2006,27(1):21-24. |
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| Authors: | XIA Tie-cheng ZHAO Wen-ying ZHANG Jiao |
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| Institution: | 1. Department of Mathematics,Shanghai University,Shanghai 200436,China;2. Department of Mathematics.,Bohai University,Jinzhou 121013,China |
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| Abstract: | A new algebraic system X is constructed by using the known loop algebra ^~A1 and difference operators. Then a new isospectral problem is established by taking advantage of X. As a result a new I.ax integrable lattice hierarchy is obtained. Furthermore, by constructing an expanding algebraic system ^~X ,the integrable couplings system of the Cubic Voherra lattice hierarchy is worked out. The method can also be applied to other lattice equation hierarchies. |
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| Keywords: | algebraic system cubic voherra lattice hierarchy integrable couplings system |
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