Solutions of mKdV in Classes of Functions Unbounded at Infinity
Solutions of mKdV in Classes of Functions Unbounded at Infinity
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无穷大无界函数类中 mKdV 的解
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Topalov
中科院分区：
文献类型：
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作者：
T. Kappeler;P. Perry;M. Shubin;P. Topalov
使用P.拉克斯的拉克斯对的概念，我们证明了整体存在性和唯一性的解决方案的初始值问题的mKdV类的光滑函数，可以在无穷远无界，特别是，可能趋于无穷远的空间变量。此外，我们还建立了这几类势函数在KdV流下的谱不变性和薛定谔算子的幺正型，以及在mKdV流下的阻抗算子的谱不变性和阻抗算子的幺正型.
Using P. Lax’s concept of a Lax pair we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and in particular, may tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schrödinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.