Geometry of nonlinear differential equations

Vinogradov, A. M.

doi:10.1007/bf01084594

Cited by 68 publications

(74 citation statements)

References 13 publications

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“…Skew-orthogonal distributions. Following [21], we show that a hyperbolic Monge-Ampère equation is equivalent to a pair of skew-orthogonal two-dimensional distributions in the Cartan distribution on J 1 τ . Let θ 1 be an arbitrary point of J 1 τ .…”

Section: More Precisely It Takes Values In Immentioning

confidence: 96%

Differential invariants of generic hyperbolic Monge-Ampère equations

2007

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Section: More Precisely It Takes Values In Immentioning

confidence: 96%

Differential invariants of generic hyperbolic Monge-Ampère equations

2007

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“…Let x, y, u, y x , u x , y xx , u xx be canonical coordinates on J 2 (1, 2) (see [21]). This means that the Cartan forms have the following coordinate representations:…”

Section: Addmissible Feedback Transformationsmentioning

confidence: 99%

“…An alternative approach is the formal one proposed by Kang in [17] and further studied in [18]- [20]. In this paper we employ the approach based on differential invariants introduced in [21] and developed in [22].…”

Section: Introductionmentioning

confidence: 99%

Differential invariants of feedback transformations for quasi-harmonic oscillation equations

Gritsenko

Kiriukhin

2017

Journal of Geometry and Physics

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The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie pseudo-group of local feedback transformations. In particular, considered class describes behavior of conservative mechanical systems. We construct the class of rational differential invariants that separate regular orbits. It is well known that differential invariants form algebra with respect to the operation of addition and multiplication [1]. In our case, constructed rational differential operators form a field (in algebraic sense). Rational differential invariants were studied by M. Rosenlicht [2,3], B. Kruglikov and V. Lychagin [4].

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“…It can be formulated geometrically as a tangency to the Cartan distribution [9], or algebraically [6] through the Whitney functional.…”

Section: Extendible Jet-functions Any Function F ∈ Cmentioning

confidence: 99%