Results 11 to 20 of about 505,503 (271)
A New Algorithm for Finding Rational First Integrals of Polynomial Vector Fields [PDF]
Qualitative Theory of Dynamical Systems, 2010 We present a new method to compute rational first integrals of planar polynomial vector fields. The algorithm is in general much faster than the usual methods and also allows to compute the remarkable curves associated to the rational first integral of the system.
Ferragut Amengual, Antoni Manel +1 more
openaire +5 more sources
Discrete & Continuous Dynamical Systems - A, 2013 In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous polynomial differential system can be transformed into a differential system of the form u˙ = uf(v), ˙v = g(v) with f(v) and g(v)
Giné, Jaume +2 more
exaly +8 more sources
Darboux Linearization and Isochronous Centers with a Rational First Integral
Journal of Differential Equations, 1997 The authors consider the following planar system \[ \dot x = -y + \sum_{i+j=2}^{n} a_{ij}x^i y^j ,\quad \dot y = x + \sum_{i+j=2}^{n} b_{ij}x^i y^j ,\quad\quad (x,y)\in \mathbb{R}^2 \tag{1} \] where \(a_{ij}\) and \(b_{ij}\) are real numbers. Let the system (1) has a center, and let \(T\) be a period-function, i.e.
Mardešić, P. +2 more
openaire +4 more sources
Trends in Computational and Applied Mathematics, 2023 The calculation of the Coulomb Potential corresponding to the product of two Exponential Type Functions, inherently has numerical challenges that must be resolved.
C. J. Alturria Lanzardo +4 more
doaj +1 more source
Controllability and optimal speed-in-action of linear systems with boundary conditions [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The paper proposes a method for solving the problem of optimal performance for linear systems of ordinary differential equations in the presence of phase and integral restrictions, when the initial and final states of the system are elements of ...
S. Aisagaliev, G.T. Korpebay
doaj +3 more sources
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
doaj +1 more source
The field of rational constants of the Volterra derivation; pp. 133–135 [PDF]
Proceedings of the Estonian Academy of Sciences, 2014 We describe the field of rational constants of the four-variable Volterra derivation. Thus, we determine all rational first integrals of its corresponding system of differential equations. Such derivations play a role in population biology, laser physics,
Janusz Zieliński
doaj +1 more source
New solitary electrostatic structures for Zakharov model in subsonic limit for solar-wind
Results in Physics, 2022 A theoretical study of Zakharov model in subsonic limit has been investigated for plasma waves solutions via many solitary and huge structures. The electrostatic field modulations, the first integral and the rational self-focusing nonlinearly methods ...
A. Almutairi +3 more
doaj +1 more source
Darboux and Analytic First Integrals of Kingni–Jafari System with Only One Stable Equilibrium Point.
Zanco Journal of Pure and Applied Sciences, 2020 In this paper, we illustrate by an evidence that the Kingni–Jafari differential system where and are real parameters has no Darboux and rational first integrals for any value of Furthermore, we show that this system has no global first integrals ...
Shno F. Muhammed +2 more
doaj +3 more sources
Generalized rational first integrals of analytic differential systems
Journal of Differential Equations, 2011 In this paper we mainly study the necessary conditions for the existence of functionally independent generalized rational first integrals of ordinary differential systems via the resonances. The main results extend some of the previous related ones, for instance the classical Poincar 's one \cite{Po}, the Furta's one, part of Chen's ones, and the Shi ...
Cong, Wang, Llibre, Jaume, Zhang, Xiang
openaire +6 more sources