| Liouville方程的Lax表述和无穷多守恒律 |
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| 引用本文： | 吴平锋,熊庄,周焕强. Liouville方程的Lax表述和无穷多守恒律[J]. 四川师范大学学报(自然科学版), 1990, 0(4) |
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| 作者姓名： | 吴平锋 熊庄 周焕强 |
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| 作者单位： | 四川师范大学物理系固体物理所(吴平锋，熊庄)，四川师范大学物理系固体物理所(周焕强) |
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| 摘 要： | 研究表明,Liouville方程至少容许两种不同的Lax表述,由每一种表述可以导出方程的一个彼此处于对合之中的守恒量的无穷集.然而,属于不同集的守恒量彼此之间不存在对合关系.此外,我们还证明,守恒量的这两个集合可以分别用具有零Poisson 括号的Virasoro 生成元的多项式函数的无穷集,即Korteweg-de Vries(KdV)集和Caudrey-Dodd-Gibbon-Sawada-Kotera(CDGSK)集表示.
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| 关 键 词： | Liouville方程 Lax表述 守恒量 对合 Virasoro生成元 KdV集 CDGSK集 |
LAX REPRESENTATIONS AND INFINITE CONSERVATION LAWS OF THE LIOUVILLE EQUATION |
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| Wu Pingfeng Xiong Zhuang Zhou Huanqiang. LAX REPRESENTATIONS AND INFINITE CONSERVATION LAWS OF THE LIOUVILLE EQUATION[J]. Journal of Sichuan Normal University(Natural Science), 1990, 0(4) |
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| Authors: | Wu Pingfeng Xiong Zhuang Zhou Huanqiang |
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| Abstract: | It is shown that the Liouville equation admits at least two different Lax representations.From each representationone may deduce an infinite sequence of conserved quantities that are in involution with each other.However,there is nosuch an involutive relation among the conserved quantities beionging to different sequences.Furthermore,it is aiso shownthat both sequences of the conserved quantities may be expressed in terms of infinite sequences of polynomial functions ofthe Virasoro generators with vanishing Poisson brackets,i,e.,KdV sequence and CDGSK sequence,respectively. |
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| Keywords: | Liouville equation Lax representations conserved quantities involution Virasoro generators KdV sequence CDGSK sequence |
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