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Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education.ORCID iD: 0000-0003-0930-7116
Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego w Kielcach, Poland.
2018 (English)Report (Other academic)
Abstract [en]

The first main aim of this article is to derive an explicit solution formula for the scalar 2d-Toda lattice depending on three independent operator parameters, ameliorating work in [29]. This is achieved by studying a noncommutative version of the two-dimensional Toda lattice, generalizing its soliton solution to the noncommutative setting.

The purpose of the applications part is to show that the family of solutions obtained from matrix data exhibits a rich variety of asymptotic behaviour. The first indicator is that web structures, studied extensively in the literature, see [4] and references therein, are a subfamily. Then three further classes of solutions (with increasingly unusual behaviour) are constructed, and their asymptotics are derived. 

Place, publisher, year, edition, pages
2018. , p. 35
Series
Mid Sweden Mathematical Reports ; 2
Keywords [en]
2d Toda lattice, asymptotic behaviour, operator identities, multiple pole solutions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-35283ISBN: 978-91-88527-86-8 (print)OAI: oai:DiVA.org:miun-35283DiVA, id: diva2:1272182
Available from: 2018-12-18 Created: 2018-12-18 Last updated: 2018-12-19Bibliographically approved

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NilsonSchiebold(5451 kB)129 downloads
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Nilson, TomasSchiebold, Cornelia

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CiteExportLink to record
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