Results 141 to 150 of about 160,056 (177)

On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2020
We present the complete classification of irreducible invariant algebraic curves of quadratic Liénard differential equations. We prove that these equations have irreducible invariant algebraic curves of unbounded degrees, in contrast with what is wrongly
M. Demina, C. Valls
semanticscholar   +1 more source

Detecting Order and Chaos by the mLE, SALI and GALI Methods in Three-Dimensional Nonlinear Yang-Mills System

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2022
The main objective of this study is to explore the nonlinear dynamics and chaos detecting in the three-dimensional (3D) generalized Hamiltonian Yang–Mills system as coupled quartic oscillators. We investigate its Liouvillian integrability. The integrable
W. Chatar, Mohammed El Ghamari, J. Kharbach, M. Benkhali, R. Masrour, A. Rezzouk, M. Ouazzani-Jamil   +6 more
semanticscholar   +1 more source

Symbolic Computations of First Integrals for Polynomial Vector Fields

Foundations of Computational Mathematics, 2017
In this article, we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing, if it exists, a rational, Darbouxian, Liouvillian or Riccati ...
Guillaume Chèze, Thierry Combot
semanticscholar   +1 more source

Linearizability conditions for the Rayleigh-like oscillators

, 2020
In this work we consider a family of nonlinear oscillators that is cubic with respect to the first derivative. Particular members of this family of equations often appear in numerous applications.
D. Sinelshchikov
semanticscholar   +1 more source

Determining Liouvillian first integrals for dynamical systems in the plane and an integrability analysis

Computer Physics Communications, 2014
Here we deal with a semi-algorithm to find Liouvillian first integrals of dynamical systems in the plane. The algorithm is based on a Darboux-type procedure to find the integrating factor for the system. The particular form of such systems allows reducing them to a single rational first order ordinary differential equation (rational 1ODE).
J. Avellar, M.S. Cardoso, L.G.S. Duarte, L.A.C.P. da Mota   +3 more
openaire   +1 more source

Path integral formalism of open quantum systems with non-diagonal system-bath coupling

Communications in Theoretical Physics
Most path integral expressions for quantum open systems are formulated with diagonal system-bath coupling, where the influence functional is a functional of scalar-valued trajectories. This formalism is enough if only a single bath is under consideration.
Ruofan Chen
semanticscholar   +1 more source

Analysing the structure of the integrating factors for first-order ordinary differential equations with Liouvillian functions in the solution

Journal of Physics A: Mathematical and General, 2002
Summary: Here, the authors demonstrate a theorem concerning the general structure of the integrating factor for first-order ordinary differential equations whose solutions contain Liouvillian functions. This result assures the generality of a method presented in a forthcoming paper of the authors [A method to tackle first-order ordinary differential ...
Duarte, L. G. S., Duarte, S. E. S., da Mota, L. A. C. P.   +2 more
openaire   +1 more source

Generalized ODE reduction algorithm for bounded degree transformation

arXiv.org
The integrability problem of rational first-order ODEs $y^{\prime}=\frac{M(x,y)}{N(x,y)}$, where $M,N \in \mathbb{R}[x,y]$ is a long-term research focus in the area of dynamical systems, physics, etc.
Shaoxuan Huang
semanticscholar   +1 more source

An efficient way to determine Liouvillian first integrals of rational second order ordinary differential equations

Computer Physics Communications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L.G.S. Duarte, J.C. Eiras, L.A.C.P. da Mota   +2 more
openaire   +2 more sources

Liouvillian integrability of some quadratic Liénard polynomial differential systems

Rendiconti del Circolo Matematico di Palermo Series 2, 2018
C. Valls
semanticscholar   +2 more sources