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Linear differential Lappo-Danilevskii systems

S. A. Mazanik (2002)

Mathematica Bohemica

The class of linear differential systems with coefficient matrices which are commutative with their integrals is considered. The results on asymptotic equivalence of these systems and their distribution among linear systems are given.

The moving frames for differential equations. II. Underdetermined and functional equations

Václav Tryhuk, Oldřich Dlouhý (2004)

Archivum Mathematicum

Continuing the idea of Part I, we deal with more involved pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ = L ( x ) y , z ¯ = M ( x ) z , ... applied to the first order differential equations including the underdetermined case (i.e. the Monge equation y ' = f ( x , y , z , z ' ) ) and certain differential equations with deviation (if z = y ( ξ ( x ) ) is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the...

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