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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

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Czech description

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Type

J_imp - 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

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

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

Name of the periodical

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Volume of the periodical

539

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

51

Pages from-to

„128543-1“-„128543-51“

UT code for WoS article

001258348400001

EID of the result in the Scopus database

2-s2.0-85195081035