Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F24%3AA0000166" target="_blank" >RIV/47813059:19610/24:A0000166 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S1007570424001011" target="_blank" >https://www.sciencedirect.com/science/article/pii/S1007570424001011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cnsns.2024.107915" target="_blank" >10.1016/j.cnsns.2024.107915</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation

Popis výsledku v původním jazyce

Applying an original megaideal-based version of the algebraic method, we compute the pointsymmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation. This is the first example of this kind in the literature, where there is no need to use the direct method for completing the computation. The analogous studies are also carried out for the corresponding nonlinear Lax representation and the dispersionless counterpart of the symmetric Nizhnik system. We also first apply the megaideal-based version of the algebraic method to find the contact-symmetry (pseudo)group of a partial differential equation. It is shown that the contact-symmetry pseudogroup of the dispersionless Nizhnik equation coincides with the first prolongation of its point-symmetry pseudogroup. We check whether the subalgebras of the maximal Lie invariance algebra of the dispersionless Nizhnik equation that naturally arise in the course of the above computations define the diffeomorphisms stabilizing this algebra or its first prolongation. In addition, we construct all the third-order partial differential equations in three independent variables that admit the same Lie invariance algebra. We also find a set of geometric properties of the dispersionless Nizhnik equation that exhaustively defines it.

Název v anglickém jazyce

Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation

Popis výsledku anglicky

Applying an original megaideal-based version of the algebraic method, we compute the pointsymmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation. This is the first example of this kind in the literature, where there is no need to use the direct method for completing the computation. The analogous studies are also carried out for the corresponding nonlinear Lax representation and the dispersionless counterpart of the symmetric Nizhnik system. We also first apply the megaideal-based version of the algebraic method to find the contact-symmetry (pseudo)group of a partial differential equation. It is shown that the contact-symmetry pseudogroup of the dispersionless Nizhnik equation coincides with the first prolongation of its point-symmetry pseudogroup. We check whether the subalgebras of the maximal Lie invariance algebra of the dispersionless Nizhnik equation that naturally arise in the course of the above computations define the diffeomorphisms stabilizing this algebra or its first prolongation. In addition, we construct all the third-order partial differential equations in three independent variables that admit the same Lie invariance algebra. We also find a set of geometric properties of the dispersionless Nizhnik equation that exhaustively defines it.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Communications in Nonlinear Science and Numerical Simulation

ISSN

1007-5704

e-ISSN

1878-7274

Svazek periodika

132

Číslo periodika v rámci svazku

May

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

19

Strana od-do

„107915-1“-„107915-19“

Kód UT WoS článku

001198218800001

EID výsledku v databázi Scopus

2-s2.0-85185836496