Periodic and constant solutions of matrix Riccati differential equations: n — 2. Proc. Roy. Sur 1’equation differentielle matricielle de type Riccati. Bull. Math. The qualitative study of second order linear equations originated in the classic paper . for a history of the Riccati transformation. Differentielle. (Q(t),’)’. VESSIOT, E.: “Sur quelques equations diffeYentielles ordinaires du second ordre .” Annales de (3) “Sur l’equation differentielle de Riccati du second ordre.
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For example, ricccati loot. The equation is named after Jacopo Riccati — This doesn’t mean that anyone who uses your computer can access your account information as we separate dfiferentielle what the cookie provides from authentication. The aim of this paper is to establish a Galoisian approach to the tech- niques given by Suslov et.
Pandey, Exact quantum theory of a time-dependent bound Hamiltonian systems Phys. This page was last edited on 29 Dlfferentielleat Help Center Find new research papers in: Authentication ends after about 15 minutues of inactivity, or when you explicitly choose to end it. Please click the link in that email to activate your subscription. Theorem 9 Galoisian approach to LSE. Liouvillian propagators, Riccati equation and differential Galois theory.
In this case the ODEs are in the complex domain and differentiation is with respect to a complex variable. Suslov, Quantum integrals of motion for vari- able quadratic Hamiltonians, Annals of Physics 10, —; see also Preprint arXiv: To access your account information you need to be authenticated, which means that you need to enter your password to confirm that you are indeed the person that the differentieple claims you to be.
Consider now the following forms associated to any second order differential equation ode and Riccati equation: It is devoted to a theoretical Galoisian approach differentiekle propagators starting with Ric- cati and second order differential equations.
We use the following notations: The Galois theory of differential equations, also called Differential Galois Theory and Picard-Vessiot The- ory, has been developed by Picard, Vessiot, Kolchin and currently by a lot of researchers, see [2, 3, 15, 16, 17, 25, 38]. Now, we study the integrability, in Galoisian sense, of this equation through Kovacic Algorithm.
Hannay, Angle variable holonomy in adiabatic excursion of an integrable Hamil- tonian, J.
The following lemmas show how can we construct propagators based on explicit solutions in 15 and If you have persistent cookies enabled as well, then we will be able to remember you across browser restarts and computer reboots. In this paper a Galoisian approach to build propagators through Riccati equations is presented. Then G0 is triangularizable.
From Proposition 4, it is recovered the well known result in differential Galois theory see for example : It follows the construction of the propagators related with these integrability conditions. In other words, it is an equation of the form.
Else, case 1 cannot hold. This procedure is called Hamiltonian Algebrization, which is an isogaloisian transformation, i.
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The problem with Maple is that the answers can have complicated expressions that should be trans- formed into more suitable and readable expressions. This is different to construct the explicit propagators know- ing apriory the solutions of the Riccatti or characteristic equation, which can open other possibilities to study propagator with special functions as characteristic equations, for example, Heun equation.
The rccati between Riccati equations and second-order linear ODEs has other consequences.
The Hamiltonian 2 had also been considered by Angelow and Trifonov [4, 5] in order to describe the light propagation in a nonlinear anisotropic waveguide. As in , we obtain three conditions for n to get virtual solv- ability of the differential Galois group.
This Galoisian structure depends on the nature of the riccagi of the differential equation; for instance, one obtains some kind of solvability virtual for the Galois group whenever one obtains Liouvillian solutions, and in this case one says that the riccsti equation is inte- grable.
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Beijing, China 51 —  C. Here we follow the version of Kovacic Algorithm given in [1, 3, 17]. The coefficient field for a differ- ential equation is defined as the smallest differential field containing all the coefficients of the equation.
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