A NEW CLASS OF REFLECTIONLESS SECOND-ORDER A∆OS AND ITS RELATION TO NONLOCAL SOLITONS
A NEW CLASS OF REFLECTIONLESS SECOND-ORDER A∆OS AND ITS RELATION TO NONLOCAL SOLITONS
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一类新的无反射二阶AΔOS及其与非局域孤子的关系
DOI：
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发表时间：
2002
期刊：
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通讯作者：
S. Ruijsenaars
中科院分区：
文献类型：
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作者：
S. Ruijsenaars
研究了一类广泛的二阶解析差分算子，该算子具有无反射特征函数。我们的A∆o的特征值方程可以看作是Shabat研究的离散谱问题的解析模拟。此外，我们与A∆o相关联的非局部孤子演化方程是Boiti和同事最近与Shabat问题相关联的离散方程的解析版本。证明了非局部孤子G（x, t）对于(x, t)∈R是正的，并证明了相应的A∆Os可以被重新解释为L（R, dx）上的自伴随算子。在适当的尺度限制下，出现KdV孤子和无反射薛定谔算子。
We study an extensive class of second-order analytic difference operators admitting reflectionless eigenfunctions. The eigenvalue equation for our A∆Os may be viewed as an analytic analog of a discrete spectral problem studied by Shabat. Moreover, the nonlocal soliton evolution equation we associate to the A∆Os is an analytic version of a discrete equation Boiti and coworkers recently associated to Shabat’s problem. We show that our nonlocal solitons G(x, t) are positive for (x, t) ∈ R and obtain evidence that the corresponding A∆Os can be reinterpreted as self-adjoint operators on L(R, dx). In a suitable scaling limit the KdV solitons and reflectionless Schrodinger operators arise.