Equivalence and symmetries of second-order differential equations

In: Mathematica Slovaca, vol. 58, no. 5

Václav Tryhuk - O. Dlouhý

Detaily:

Rok, strany: 2008, 541 - 566

Kľúčové slová:

differential equations with deviations, equivalence of differential equations, symmetry of differential equation, differential invariants, moving frames

O článku:

In this article we investigate the equivalence of underdetermined differential equations and differential equations with deviations of second order with respect to the pseudogroup of transformations $\bar x=φ (x)$, $\bar y=\bar y(\bar x)=L(x)+y(x)$, $\bar z=\bar z(\bar x)=M(x)+z(x)$. Our main aim is to determine such equations that admit a large pseudogroup of symmetries. Instead the common direct calculations, we use some more advanced tools from differential geometry, however, our exposition is self-contained and only the most fundamental properties of differential forms are employed.

Ako citovať:

ISO 690:

Tryhuk, V., Dlouhý, O. 2008. Equivalence and symmetries of second-order differential equations. In Mathematica Slovaca, vol. 58, no.5, pp. 541-566. 0139-9918.

APA:

Tryhuk, V., Dlouhý, O. (2008). Equivalence and symmetries of second-order differential equations. Mathematica Slovaca, 58(5), 541-566. 0139-9918.