Displaying similar documents to “The moving frames for differential equations. I. The change of independent variable”

Equivalence and symmetries of first order differential equations

V. Tryhuk (2008)

Czechoslovak Mathematical Journal

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In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ = y ¯ ( x ¯ ) = L ( x ) y ( x ) . That means, the transformed unknown function y ¯ is obtained by means of the change of the independent variable and subsequent multiplication by a nonvanishing factor. Instead of the common direct calculations, we use some more advanced tools from differential...

Examples from the calculus of variations. IV. Concluding review

Jan Chrastina (2001)

Mathematica Bohemica

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Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined...