Solutions of Second-Order PDEs with First-Order Quotients

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Solutions of Second-Order PDEs with First-Order Quotients

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Solutions of Second-Order PDEs with First-Order Quotients

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-14466Y" target="_blank" >GJ19-14466Y: Speciální metriky v supergravitaci a nové G-struktury</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

LOBACHEVSKII JOURNAL OF MATHEMATICS

ISSN

1995-0802

e-ISSN

—

Svazek periodika

41

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

19

Strana od-do

2491-2509

Kód UT WoS článku

000617462200022

EID výsledku v databázi Scopus

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