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Cauchy-type determinants and integrable systems
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
2010 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 433, no 2, p. 447-475Article in journal (Refereed) Published
Abstract [en]

It is well known that the Sylvester matrix equation AX + XB = C has a unique solution X if and only if 0 ∉ spec(A) + spec(B). The main result of the present article are explicit formulas for the determinant of X in the case that C is one-dimensional. For diagonal matrices A, B, we reobtain a classical result by Cauchy as a special case. The formulas we obtain are a cornerstone in the asymptotic classification of multiple pole solutions to integrable systems like the sine-Gordon equation and the Toda lattice. We will provide a concise introduction to the background from soliton theory, an operator theoretic approach originating from work of Marchenko and Carl, and discuss examples for the application of the main results.

Place, publisher, year, edition, pages
2010. Vol. 433, no 2, p. 447-475
Keywords [en]
Cauchy-type determinants; Integrable systems; Multiple-pole solutions; Sylvester equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-11692DOI: 10.1016/j.laa.2010.03.011ISI: 000278434100013Scopus ID: 2-s2.0-77953138087OAI: oai:DiVA.org:miun-11692DiVA, id: diva2:324047
Available from: 2010-06-14 Created: 2010-06-14 Last updated: 2017-12-12Bibliographically approved

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Schiebold, Cornela

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