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From the non-abelian to the scalar two-dimensional Toda lattice
Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences.
##### Responsible organisation
2005 (English)In: Glasgow Mathematical Journal, ISSN 0017-0895, E-ISSN 1469-509X, Vol. 47, no A, 177-189 p.Article in journal (Refereed) Published
##### Abstract [en]

We extend a solution method used for the one-dimensional Toda lattice in [1], [2] to the two-dimensional Toda lattice. The idea is to study the lattice not with values in $\mathbb{C}$ but in the Banach algebra ${\cal L}$ of bounded operators and to derive solutions of the original lattice ($\mathbb{C}$-solutions) by applying a functional $\tau$ to the ${\cal L}$-solutions constructed in 1. The main advantage of this process is that the derived solution still contains an element of $\cal L$ as parameter that may be chosen arbitrarily. Therefore, plugging in different types of operators, we can systematically construct a huge variety of solutions. In the second part we focus on applications. We start by rederiving line-solitons and briefly discuss discrete resonance phenomena. Moreover, we are able to find conditions under which it is possible to superpose even countably many line-solitons.

##### Place, publisher, year, edition, pages
2005. Vol. 47, no A, 177-189 p.
##### Keyword [en]
two-dimensional Toda lattice, nonlinear superposition
Mathematics
##### Identifiers
Local ID: 5431OAI: oai:DiVA.org:miun-4450DiVA: diva2:29482
Available from: 2008-09-30 Created: 2009-01-07 Last updated: 2017-12-12Bibliographically approved

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#### Authority records BETA

Schiebold, Cornelia

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Department of Natural Sciences
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Glasgow Mathematical Journal
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Cite
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