2D reductions of the equation u_{yy} = u_{tx} + u_{y}u_{xx} - u_{x}u_{xy} and their nonlocal symmetries

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F17%3AA0000034" target="_blank" >RIV/47813059:19610/17:A0000034 - isvavai.cz</a>
Result on the web
<a href="https://www.tandfonline.com/doi/abs/10.1080/14029251.2017.1418052" target="_blank" >https://www.tandfonline.com/doi/abs/10.1080/14029251.2017.1418052</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/14029251.2017.1418052" target="_blank" >10.1080/14029251.2017.1418052</a>

Result language
angličtina
Original language name
2D reductions of the equation u_{yy} = u_{tx} + u_{y}u_{xx} - u_{x}u_{xy} and their nonlocal symmetries
Original language description
We consider the 3D equation u_{yy}= u_{tx} + u_y u_{xx} - u_x u_{xy} and its 2D symmetry reductions: (1) u_{yy} = (u_y + y) u_{xx} - u_{x} u_{xy} - 2 (which is equivalent to the Gibbons-Tsarev equation) and (2) u_{yy} = (u_y + 2x) u_{xx} + (y - u_{x}) u{xy} - u_{x}. Using the corresponding reductions of the known Lax pair for the 3D equation, we describe nonlocal symmetries of (1) and (2) and show that the Lie algebras of these symmetries are isomorphic to the Witt algebra.
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
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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