Hamiltonian Systems and Sturm–Liouville Equations: Darboux Transformation and Applications

被引：0
作者：
Alexander Sakhnovich
机构：
[1] Universität Wien,Fakultät für Mathematik
来源：
Integral Equations and Operator Theory | 2017年 / 88卷
关键词：
Hamiltonian system; Sturm–Liouville equation; Darboux transformation; Primary 34B24; 34L15; 47E05; Secondary 34B20; 74H05;
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摘要：
We introduce GBDT version of Darboux transformation for Hamiltonian and Shin–Zettl systems as well as for Sturm–Liouville equations (including indefinite Sturm–Liouville equations). These are the first results on Darboux transformation for general-type Hamiltonian and for Shin–Zettl systems. The obtained results are applied to the corresponding transformations of the Weyl–Titchmarsh functions and to the construction of explicit solutions of dynamical systems, of two-way diffusion equations and of indefinite Sturm–Liouville equations. The energy of the explicit solutions of dynamical systems is expressed (in a quite simple form) in terms of the parameter matrices of GBDT. The insertion of non-real eigenvalues into the spectrum of indefinite Sturm–Liouville operators is studied.
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页码：535 / 557
页数：22
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