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BY-NC-ND 3.0 license Open Access Published by De Gruyter August 27, 2008

Equivalence and symmetries of second-order differential equations

  • V. Tryhuk EMAIL logo and O. Dlouhý
From the journal Mathematica Slovaca


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), ȳ = ȳ($$ \bar x $$) = 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.

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Published Online: 2008-8-27
Published in Print: 2008-10-1

© 2008 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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