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Nonlinear equations in soliton physics and operator ideals
Universit├Ąt Jena.
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
1999 (English)In: Nonlinearity, ISSN 0951-7715, Vol. 12, no 2, 333-364 p.Article in journal (Refereed) Published
Abstract [en]

An operator-theoretic method for the investigation of nonlinear equations in soliton physics is discussed comprehensively. Originating from pioneering work of Marchenko, our operator-method is based on new insights into the theory of traces and determinants on operator ideals. Therefore, we give a systematic and concise approach to some recent developments in this direction which are important in the context of this paper. Our method is widely applicable. We carry out the corresponding arguments in detail for the Kadomtsev-Petviashvili equation and summarize the results concerning the Korteweg-de Vries and the modified Korteweg-de Vries equation as well as for the sine-Gordon equation. Exactly the same formalism works in the discrete case, as the treatment of the Toda lattice, the Langmuir and the Wadati lattice shows.

Place, publisher, year, edition, pages
1999. Vol. 12, no 2, 333-364 p.
Keyword [en]
soliton equations, traces and determinants on quasi-Banach ideals
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-4445DOI: 10.1088/0951-7715/12/2/012Local ID: 5427OAI: oai:DiVA.org:miun-4445DiVA: diva2:29477
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2009-03-19Bibliographically approved

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