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Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3 [PDF]
Rocky Mountain Journal of Mathematics, 2007 Altres ajuts: ICREA Academia We classify all of the weight-homogeneous planar polynomial differential systems of weight degree 4 having a polynomial first integral.
L. Cairó, J. Llibre
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Polynomial differential systems having a given Darbouxian first integral
Bulletin des Sciences Mathématiques, 2004 The Darbouxian theory of integrability allows to determine when a polynomial differential system in C2 has a first integral of the kind f λ1 1 ···f λp p exp(g/h) where fi , g and h are polynomials in C[x, y], and λi ∈ C for i = 1, . . . ,p. The functions of this form are called Darbouxian functions. Here, we solve the inverse problem, i.e.
J. Llibre, C. Pantazi
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A class of polynomial planar vector fields with polynomial first integral [PDF]
Journal of Mathematical Analysis and Applications, 2014 We give an algorithm for deciding whether a planar polynomial differential system has a first integral which factorizes as a product of defining polynomials of curves with only one place at infinity.
Antoni Ferragut +2 more
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On the polynomial differential systems having polynomial first integrals
Bulletin des Sciences Mathématiques, 2012 We consider the class of complex planar polynomial differential systems having a polynomial first integral. Inside this class the systems having minimal polynomial first integrals without critical remarkable values are the Hamiltonian ones. Here we mainly study the subclass of polynomial differential systems such that their minimal polynomial first ...
Belen García +2 more
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On the existence of polynomial first integrals of quadratic homogeneous systems of ordinary differential equations [PDF]
, 2000 We consider systems of ordinary differential equations with quadratic homogeneous right hand side. We give a new simple proof of a result already obtained in [8,10] which gives the necessary conditions for the existence of polynomial first integrals. The
Tsygvintsev, Alexei
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Polynomial first integrals of quadratic vector fields
Journal of Differential Equations, 2006 The goal of this paper is to characterize those quadratic differential equations in the plane having a polynomial first integral, and to provide an explicit expression of these systems as well as of their polynomial first integrals. It is well known that if the system writes as \[ \dot x=P(x,y), \quad \dot y=Q(x,y) \] it is not restrictive to assume ...
J. Chavarriga +4 more
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Polynomial first integrals via the Poincaré series
Journal of Computational and Applied Mathematics, 2005 The author determines polynomial ordinary differential systems which have a polynomial first integral. One typical result is Theorem 5: The system \[ \begin{aligned} \dot{x}= -y + \lambda _2x^3+ \lambda_3 x^2y + \lambda _4 xy^2 + \lambda _5 y^3, \\ \dot{y}= x + \lambda _6x^3+ \lambda_7 x^2y - \lambda _3 xy^2 + \lambda _8 y^3, \end{aligned} \] has a ...
J. Giné
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Symbolic Computations of First Integrals for Polynomial Vector Fields [PDF]
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
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Symmetry properties of a generalized Korteweg-de Vries equation and some explicit solutions [PDF]
International Journal of Mathematics and Mathematical Sciences, 2005 The symmetry group method is applied to a generalized Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this technique. Polynomial, trigonometric, and elliptic function solutions can be calculated.
Paul Bracken
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On planar polynomial vector fields with elementary first integrals [PDF]
Journal of Differential Equations, 2019 We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class.
C. Christopher +3 more
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