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引用次数: 0
摘要
我们考虑了 C 型多组分卡多姆采夫-彼得维亚什维利层次结构（多组分 CKP 层次结构），它最初是借助矩阵伪差分算子通过拉克斯-萨托形式主义定义的。从波函数的双线性关系出发，我们证明了多组分 CKP 层次的 tau 函数的存在，并提供了一个通过 tau 函数表达波函数的公式。我们还发现了这个 tau 函数与多组分卡多姆采夫-彼得维亚什维利层次结构的 tau 函数之间的关系。多组分 CKP 层次的 tau 函数满足一种积分关系，与后者 tau 函数的积分关系不同，它不再是双线性的，而是具有更复杂的形式。
We consider multi-component Kadomtsev-Petviashvili hierarchy of type C (the multi-component CKP hierarchy) originally defined with the help of matrix pseudo-differential operators via the Lax-Sato formalism. Starting from the bilinear relation for the wave functions, we prove existence of the tau-function for the multi-component CKP hierarchy and provide a formula which expresses the wave functions through the tau-function. We also find how this tau-function is related to the tau-function of the multi-component Kadomtsev-Petviashvili hierarchy. The tau-function of the multi-component CKP hierarchy satisfies an integral relation which, unlike the integral relation for the latter tau-function, is no longer bilinear but has a more complicated form.
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MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas.
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