圆上布森斯方程的拉克斯对中的（L）-操作者的逆问题

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-10-14 DOI:10.1134/S0016266324030092

Andrey Badanin, Evgeny Korotyaev

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引用次数: 0

摘要

我们考虑了一个三阶非自交算子，它是圆上布森斯克方程的拉克斯对中的（L）算子。我们构建了一个从算子系数集到谱数据集的映射，类似于 E. Korotyaev 为希尔算子构建的相应映射。我们证明，在零邻域，我们的映射是解析的、一一对应的。

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Inverse Problem for the \(L\)-Operator in the Lax Pair of the Boussinesq Equation on the Circle

We consider a third-order non-self-adjoint operator which is an \(L\)-operator in the Lax pair for the Boussinesq equation on the circle. We construct a mapping from the set of operator coefficients to the set of spectral data, similar to the corresponding mapping for the Hill operator constructed by E. Korotyaev. We prove that, in a neighborhood of zero, our mapping is analytic and one-to-one.

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来源期刊

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.