Journal of Nonlinear Mathematical Physics

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Volume 27, Issue 1, October 2019, Pages 57 - 94

Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour

Authors
Tomas Nilsona, Cornelia Schiebolda, b
aDepartment of Mathematics and Science Education, Mid Sweden University, S-851 70 Sundsvall, Sweden
bInstytut Matematyki, Uniwersytet Jana Kochanowskiego w Kielcach, Poland
Received 19 December 2018, Accepted 7 July 2019, Available Online 25 October 2019.
DOI
10.1080/14029251.2020.1683978How to use a DOI?
Abstract

The first main aim of this article is to derive an explicit solution formula for the scalar two-dimensional Toda lattice depending on three independent operator parameters, ameliorating work in [31]. This is achieved by studying a noncommutative version of the 2d-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.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Next Article In Issue>
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 1
Pages
57 - 94
Publication Date
2019/10/25
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1683978How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Tomas Nilson
AU  - Cornelia Schiebold
PY  - 2019
DA  - 2019/10/25
TI  - Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour
JO  - Journal of Nonlinear Mathematical Physics
SP  - 57
EP  - 94
VL  - 27
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1683978
DO  - 10.1080/14029251.2020.1683978
ID  - Nilson2019
ER  -