INTEGRABLE REDUCTIONS OF THE DRESSING CHAIN

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F19%3A50019994" target="_blank" >RIV/62690094:18470/19:50019994 - isvavai.cz</a>
Result on the web
<a href="https://www.aimsciences.org/article/doi/10.3934/jcd.2019014" target="_blank" >https://www.aimsciences.org/article/doi/10.3934/jcd.2019014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/jcd.2019014" target="_blank" >10.3934/jcd.2019014</a>

Result language
angličtina
Original language name
INTEGRABLE REDUCTIONS OF THE DRESSING CHAIN
Original language description
In this paper we construct a family of integrable reductions of the dressing chain, described in its Lotka-Volterra form. For each k,n is an element of N with n >= 2k +1 we obtain a Lotka-Volterra system LVb(n, k) on R-n which is a deformation of the Lotka-Volterra system LV(n, k), which is itself an integrable reduction of the 2m+1-dimensional Bogoyavlenskij-Itoh system LV(2m+1, m), where m = n - k - 1. We prove that LVb(n, k) is both Liouville and non-commutative integrable, with rational first integrals which are deformations of the rational first integrals of LV(n, k). We also construct a family of discretizations of LVb(n, 0), including its Kahan discretization, and we show that these discretizations are also Liouville and superintegrable.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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