On construction of symmetries and recursion operators from zero-curvature representations and the Darboux?Egoroff system

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F14%3A%230000454" target="_blank" >RIV/47813059:19610/14:#0000454 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0393044014001065" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0393044014001065</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.geomphys.2014.05.017" target="_blank" >10.1016/j.geomphys.2014.05.017</a>

Result language
angličtina
Original language name
On construction of symmetries and recursion operators from zero-curvature representations and the Darboux?Egoroff system
Original language description
The Darboux-Egoroff system of PDEs with any number n >= 3 of independent variables plays an essential role in the problems of describing n-dimensional flat diagonal metrics of Egoroff type and Frobenius manifolds. We construct a recursion operator and its inverse for symmetries of the Darboux-Egoroff system and describe some symmetries generated by these operators. The constructed recursion operators are not pseudodifferential, but are Backlund autotransformations for the linearized system whose solutions correspond to symmetries of the Darboux-Egoroff system. For some other PDEs, recursion operators of similar types were considered previously by Papachristou, Guthrie, Marvan, Poboril, and Sergyeyev. In the structure of the obtained third and fifth order symmetries of the Darboux-Egoroff system, one finds the third and fifth order flows of an (n - 1)-component vector modified KdV hierarchy. The constructed recursion operators generate also an infinite number of nonlocal symmetries. In
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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