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Nonlinear equations in soliton physics and operator ideals
Universität Jena.
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för naturvetenskap.
1999 (engelsk)Inngår i: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 12, nr 2, s. 333-364Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
1999. Vol. 12, nr 2, s. 333-364
Emneord [en]
soliton equations, traces and determinants on quasi-Banach ideals
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Identifikatorer
URN: urn:nbn:se:miun:diva-4445DOI: 10.1088/0951-7715/12/2/012Lokal ID: 5427OAI: oai:DiVA.org:miun-4445DiVA, id: diva2:29477
Tilgjengelig fra: 2008-09-30 Laget: 2008-09-30 Sist oppdatert: 2017-12-12bibliografisk kontrollert

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