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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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