【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.更多还原

【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.更多还原