Results 11 to 20 of about 572,208 (300)
Discrete & Continuous Dynamical Systems - A, 2015 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)
J. Giné, M. Grau, J. Llibre
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Journal of Applied Mathematics, 2015 The fractional derivatives in the sense of the modified Riemann-Liouville derivative and Feng’s first integral method are employed to obtain the exact solutions of the nonlinear space-time fractional ZKBBM equation and the nonlinear space-time fractional
Huitzilin Yépez-Martínez +2 more
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Abstract and Applied Analysis, 2013 The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and ...
Shoukry Ibrahim Atia El-Ganaini
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Darboux polynomials and first integrals of natural polynomial Hamiltonian systems [PDF]
Physics Letters A, 2004 We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function.
Maciejewski, Andrzej J. +1 more
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Darboux integrability of a hyperjerk memristive system
Zanco Journal of Pure and Applied Sciences, 2023 In this work, we investigate the following novel four-dimensional dynamical memristive system (see, (Prousalis et al., 2017)) This system, in a certain area of the parameter space, exhibits hyper-jerk dynamics and a line of singularities passing ...
Niazy Hady Hussein ,Soran Mohammed Khudur
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Polynomial and rational first integrals for planar homogeneous polynomial differential systems [PDF]
Publicacions Matemàtiques, 2021 In this paper we find necessary and suficient conditions in order that a planar homogeneous polynomial differential system has a polynomial or rational first integral. We apply these conditions to linear and quadratic homogeneous polynomial differential systems.
Giné, Jaume, Grau, Maite, Llibre, Jaume
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Interpolation rational integral fraction of the Hermitian-type on a continual set of nodes
Математичні Студії, 2021 Some approaches to the construction of interpolation rational integral approximations with arbitrary multiplicity of nodes are analyzed. An integral rational Hermitian-type interpolant of the third order on a continual set of nodes, which is the ratio of
Ya. O. Baranetskij +3 more
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Anais da Academia Brasileira de Ciências, 2021 Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of Liénard differential equations
JAUME LLIBRE +2 more
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POLYNOMIAL FIRST INTEGRALS FOR THE CHEN AND LÜ SYSTEMS [PDF]
International Journal of Bifurcation and Chaos, 2012 We characterize all the values of the parameters for which the Chen and Lü systems have polynomial first integrals by using weight homogeneous polynomials and the method of characteristics for solving partial differential equations. We improve previous results which were not complete.
Llibre, Jaume, Valls, Clàudia
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Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems [PDF]
Applied Mathematics Letters, 2009 We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polynomial transformation of variables.
Belen García +2 more
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