Solutions of Second-Order PDEs with First-Order Quotients
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017922" target="_blank" >RIV/62690094:18470/20:50017922 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1134/S1995080220120367" target="_blank" >https://link.springer.com/article/10.1134/S1995080220120367</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1134/S1995080220120367" target="_blank" >10.1134/S1995080220120367</a>
Alternative languages
Result language
angličtina
Original language name
Solutions of Second-Order PDEs with First-Order Quotients
Original language description
We investigate a general approach for solving a partial differential equation by using the differential invariants of its point symmetries. By first solving its quotient PDE, which is given by the differential syzygies in the algebra of differential invariants, we obtain new differential constraints which are compatible with the PDE under consideration. Adding these constraints to our system makes it overdetermined, and easier to solve. We focus on second-order scalar PDEs on a function of two variables whose quotients are first-order scalar PDEs. This situation occurs only when the Lie algebra of symmetries of the second-order PDE is infinite-dimensional. We apply this idea to various second-order PDEs with infinite-dimensional symmetry Lie algebras, one of which is the Hunter-Saxton equation.
Czech name
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Czech description
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Classification
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
Result continuities
Project
<a href="/en/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Special metrics in supergravity and new G-structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
LOBACHEVSKII JOURNAL OF MATHEMATICS
ISSN
1995-0802
e-ISSN
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Volume of the periodical
41
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
2491-2509
UT code for WoS article
000617462200022
EID of the result in the Scopus database
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