Results 1 to 10 of about 66 (58)
Finding Liouvillian First Integrals of Rational ODEs of Any Order in Finite Terms [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2006 It is known, due to Mordukhai-Boltovski, Ritt, Prelle, Singer, Christopher and others, that if a given rational ODE has a Liouvillian first integral then the corresponding integrating factor of the ODE must be of a very special form of a product of ...
Yuri N. Kosovtsov
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Liouvillian first integrals of second order polynomial differential equations
Electronic Journal of Differential Equations, 1999 The author proves the following theorem: If the system \[ \dot x= P(x,y),\quad \dot y= Q(x,y)\quad (P,\;Q\text{ polynomials})\tag{1} \] has a Liouvillian integrating factor of the form: \[ \exp\{\int Udx+ Vdy\},\quad U_y= V_x,\tag{2} \] where \(U\), \(V\) are rational functions of \(x\) and \(y\), then there exists a Darbouxian integrating factor of ...
Colin Christopher
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Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems [PDF]
Advanced Nonlinear Studies, 2013 Abstract We study the Liouvillian first integrals for the generalized Liénard polynomial differential systems of the form xʹ = y, yʹ = -g(x) - f(x)y, where g(x) and f(x) are arbitrary polynomials such that 2 ≤ deg g ≤ deg f.
Jaume Llibre, Clàudia Valls
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Liouvillian and Analytic First Integrals for the Brusselator System [PDF]
Journal of Nonlinear Mathematical Physics, 2012 We characterize the Liouvillian and analytic first integrals for the polynomial differential systems of the form x' = a − (b + 1)x + x2y, y' = bx − x2y, with a, b ∈ R, called the Brusselator differential systems.
Llibre, Jaume, Valls, Clàudia
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Analysis of the multi-phenomenal nonlinear system : Testing Integrability and detecting chaos
Results in Physics, 2023 As a large extension in Hamiltonian form, the system of a PT symmetric dimer of coupled nonlinear oscillators is developed. This system provides an explanation for a number of problems with Hamiltonian dynamics. Integrability is evaluated in the Painlevé
Mohamed Benkhali +6 more
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Liouvillian First Integrals for Generalized Riccati Polynomial Differential Systems [PDF]
Advanced Nonlinear Studies, 2015 Abstract We study the existence and non-existence of Liouvillian first integrals for the generalized Riccati polynomial differential systems of the form xʹ = y, yʹ = a(x)y2 +b(x)y+c(x), where a(x), b(x) and c(x) are polynomials.
Llibre, Jaume, Valls, Clàudia
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Geometry and integrability of quadratic systems with invariant hyperbolas
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Let QSH be the family of non-degenerate planar quadratic differential systems possessing an invariant hyperbola. We study this class from the viewpoint of integrability.
Regilene Oliveira +2 more
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Liouvillian first integrals for quadratic systems with an integrable saddle [PDF]
Rocky Mountain Journal of Mathematics, 2015 Agraïments: The second author was supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. We provide explicit expressions for the Liouvillian first integrals of the quadratic polynomial differential systems having an integrable saddle.
Yudy Bolaños +2 more
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An efficient method for computing Liouvillian first integrals of planar polynomial vector fields [PDF]
Journal of Differential Equations, 2021 Here we present an efficient method to compute Darboux polynomials for polynomial vector fields in the plane. This approach is restricetd to polynomial vector fields presenting a Liouvillian first integral (or, equivalently, to rational first order differential equations (rational 1ODEs) presenting a Liouvillian general solution).
L.G.S. Duarte, L.A.C.P. da Mota
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A note on Liouvillian first integrals and invariant algebraic curves
Applied Mathematics Letters, 2021 In this paper we study the existence and non-existence of finite invariant algebraic curves for complex planar polynomial differential system having a Liouvillian first integral.
Giné, Jaume +2 more
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