Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F24%3AA0000170" target="_blank" >RIV/47813059:19610/24:A0000170 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X24004657" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X24004657</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2024.128543" target="_blank" >10.1016/j.jmaa.2024.128543</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations

Popis výsledku v původním jazyce

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements parameterizing these systems. For each class from the constructed chain of nested gauged classes of such systems, we single out its singular subclass, which appears to consist of systems being similar to the elementary (free particle) system whereas the regular subclass is the complement of the singular one. This allows us to exhaustively describe the equivalence groupoids of the above classes as well as of their singular and regular subclasses. Applying various algebraic techniques, we establish principal properties of Lie symmetries of the systems under consideration and outline ways for completely classifying these symmetries. In particular, we compute the sharp lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by systems from each of the above classes and subclasses. We also show how equivalence transformations and Lie symmetries can be used for reduction of order of such systems and their integration. As an illustrative example of using the theory developed, we solve the complete group classification problems for all these classes in the case of two dependent variables.

Název v anglickém jazyce

Admissible transformations and Lie symmetries of linear systems of second-order ordinary differential equations

Popis výsledku anglicky

We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements parameterizing these systems. For each class from the constructed chain of nested gauged classes of such systems, we single out its singular subclass, which appears to consist of systems being similar to the elementary (free particle) system whereas the regular subclass is the complement of the singular one. This allows us to exhaustively describe the equivalence groupoids of the above classes as well as of their singular and regular subclasses. Applying various algebraic techniques, we establish principal properties of Lie symmetries of the systems under consideration and outline ways for completely classifying these symmetries. In particular, we compute the sharp lower and upper bounds for the dimensions of the maximal Lie invariance algebras possessed by systems from each of the above classes and subclasses. We also show how equivalence transformations and Lie symmetries can be used for reduction of order of such systems and their integration. As an illustrative example of using the theory developed, we solve the complete group classification problems for all these classes in the case of two dependent variables.

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

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

539

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

51

Strana od-do

„128543-1“-„128543-51“

Kód UT WoS článku

001258348400001

EID výsledku v databázi Scopus

2-s2.0-85195081035