Integrability in differential coverings
نویسندگان
چکیده
منابع مشابه
Integrability Estimates for Gaussian Rough Differential Equations
We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H > 1/4. We remark on the relevance of such estimates to a number of significant open...
متن کاملDiscrete differential geometry. Integrability as consistency
Since ‘nice’ and ‘interesting’ can hardly be treated as mathematically formulated features, let us discuss the permutability property. We shall explain it in more detail for the classical example of surfaces with constant negative Gaussian curvature (K-surface) with their Bäcklund transformations. Let r : R → R be a K-surface, and r10 and r01 two K-surfaces obtained by Bäcklund transformations ...
متن کاملDifferential Galois obstructions for non-commutative integrability
We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non...
متن کاملIntegrability of planar polynomial differential systems through linear differential equations . ∗
In this work, we consider rational ordinary differential equations dy/dx = Q(x, y)/P (x, y), with Q(x, y) and P (x, y) coprime polynomials with real coefficients. We give a method to construct equations of this type for which a first integral can be expressed from two independent solutions of a second–order homogeneous linear differential equation. This first integral is, in general, given by a...
متن کاملCoverings and the Fundamental Group for Partial Differential Equations
Following I. S. Krasilshchik and A. M. Vinogradov [8], we regard PDEs as infinite-dimensional manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs and Bäcklund transformations in soliton theory. We show that, similarly to usual coverings in topology, at least for some PDEs differential coverings ar...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2015
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2013.12.009