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Darboux Transformations from n-KdV to KP

机译:从n-KdV到KP的Darboux转换

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摘要

The iterated Darboux transformations of an ordinary differential operator are constructively parametrized by an infinite-dimensional Grassmannian of finitely supported distributions. In the case that the operator depends on time parameters so that it is a solution to the n-KdV hierarchy, it is shown that the transformation produces a solution of the KP hierarchy. The standard definitions of the theory of -functions are applied to this Grassmannian and it is shown that these new -functions are quotients of KP -functions. The application of this procedure for the construction of higher rank KP solutions is discussed.
机译:普通微分算子的迭代Darboux变换由有限支持分布的无穷维Grassmannian进行构造性参数化。在运算符依赖于时间参数以使其成为n-KdV层次结构的解决方案的情况下,表明该转换产生了KP层次结构的解决方案。函数理论的标准定义被应用于该格拉斯曼方程,并且表明这些新函数是KP函数的商。讨论了该程序在构建高阶KP解中的应用。

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