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Integrable Abel equations and Vein's Abel equation [PDF]
Mathematical Methods in the Applied Sciences, 2016 We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order hyperbolic ...
Stefan C Mancas, Haret C Rosu
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A complete and partial integrability technique of the Lorenz system
Results in Physics, 2018 In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage
Lazhar Bougoffa +2 more
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Dirichlet and Neumann Problems for String Equation, Poncelet Problem and Pell-Abel Equation [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2006 We consider conditions for uniqueness of the solution of the Dirichlet or the Neumann problem for 2-dimensional wave equation inside of bi-quadratic algebraic curve.
Vladimir P. Burskii, Alexei S. Zhedanov
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On Solvability of the Sonin–Abel Equation in the Weighted Lebesgue Space
Fractal and Fractional, 2021 In this paper we present a method of studying a convolution operator under the Sonin conditions imposed on the kernel. The particular case of the Sonin kernel is a kernel of the fractional integral Riemman–Liouville operator, other various types of the ...
Maksim V. Kukushkin
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Revolving scheme for solving a cascade of Abel equations in dynamics of planar satellite rotation
Theoretical and Applied Mechanics Letters, 2017 The main objective for this research was the analytical exploration of the dynamics of planar satellite rotation during the motion of an elliptical orbit around a planet. First, we revisit the results of J. Wisdom et al.
Sergey V. Ershkov
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Generalized symmetries, first integrals, and exact solutions of chains of differential equations [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 New integrability properties of a family of sequences of ordinary differential equations, which contains the Riccati and Abel chains as the most simple sequences, are studied.
C. Muriel, M. C. Nucci
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SOLVE ABEL’S INTEGRAL EQUATION USING POINT INTERPOLATION MESHLESS METHOD [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2018 In this paper the numerical method for solving Abel,s integral equation are introduced ,this method is based on point interpolation meshless method. Also Radial basis function, zeros of the shifted Legendre polynomial as the collocation points utilized ...
Nahdh. S .m. Al-saif
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Équation de Pell–Abel et applications
Comptes Rendus. Mathématique, 2022 In this paper, we show that there are solutions of degree $r$ of the equation of Pell–Abel on some real hyperelliptic curve of genus $g$ if and only if $ r > g$.
Gendron, Quentin
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Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation
Journal of Mathematics, 2022 This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix.
Ioannis Dassios +2 more
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Rational limit cycles of Abel differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2023 We study the number of rational limit cycles of the Abel equation $x'=A(t)x^3+B(t)x^2$, where $A(t)$ and $B(t)$ are real trigonometric polynomials. We show that this number is at most the degree of $A(t)$ plus one.
José Luis Bravo +2 more
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