Inverse Scattering of Canonical Systems and Their Evolution

Andrey Melnikov

doi:10.1007/s11785-014-0391-1

Inverse Scattering of Canonical Systems and Their Evolution

Andrey Melnikov

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this work we present an analogue of the inverse scattering for canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the class of functions for which the inverse scattering exists. We also derive an evolutionary equation, arising from canonical systems, which describes an evolution of the logarithmic derivative of the tau function, associated to these systems.

Original language	English
Pages (from-to)	793-819
Number of pages	27
Journal	Complex Analysis and Operator Theory
Volume	9
Issue number	4
DOIs	https://doi.org/10.1007/s11785-014-0391-1
State	Published - 1 Apr 2015
Externally published	Yes

Keywords

Canonical systems
Completely integrable PDEs
Krein spaces
Vessels

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1007/s11785-014-0391-1

Cite this

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title = "Inverse Scattering of Canonical Systems and Their Evolution",

abstract = "In this work we present an analogue of the inverse scattering for canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the class of functions for which the inverse scattering exists. We also derive an evolutionary equation, arising from canonical systems, which describes an evolution of the logarithmic derivative of the tau function, associated to these systems.",

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AB - In this work we present an analogue of the inverse scattering for canonical systems using theory of vessels and associated to them completely integrable systems. Analytic coefficients fits into this setting, significantly expanding the class of functions for which the inverse scattering exists. We also derive an evolutionary equation, arising from canonical systems, which describes an evolution of the logarithmic derivative of the tau function, associated to these systems.

KW - Canonical systems

KW - Completely integrable PDEs

KW - Krein spaces

KW - Vessels

UR - https://www.scopus.com/pages/publications/84939877379

U2 - 10.1007/s11785-014-0391-1

DO - 10.1007/s11785-014-0391-1

M3 - Article

AN - SCOPUS:84939877379

SN - 1661-8254

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EP - 819

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 4

ER -

Inverse Scattering of Canonical Systems and Their Evolution

Abstract

Keywords

ASJC Scopus subject areas

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