Results 61 to 70 of about 36,805 (178)
On the composition conjectures
Electronic Journal of Differential Equations, 2003 We describe a class of polynomials that satisfy the composition conjecture for the moments. We also show that the composition conjecture for the moments is not weaker than the composition conjecture for a center.
Mohamad A. M. Alwash
doaj
, 2004 In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric ...
Abramowitz M +22 more
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The KdV in Cosmology: a useful tool or a distraction?
, 2014 The letter is a response to the recent article by J. Lidsey. We demonstrate that the Schwarzian derivative technique developed therein is but a consequence of linearizabiliy of the original cosmological equations.
Yaparova, A. V. +2 more
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Algebraic geometry of the center-focus problem for Abel differential equations [PDF]
Ergodic Theory and Dynamical Systems, 2014 The Abel differential equation $y^{\prime }=p(x)y^{3}+q(x)y^{2}$ with polynomial coefficients $p,q$ is said to have a center on $[a,b]$ if all its solutions, with the initial value $y(a)$ small enough, satisfy the condition $y(a)=y(b)$. The problem of giving conditions on $(p,q,a,b)$ implying a center for the Abel equation is analogous to the classical
Briskin, M., Pakovich, F., Yomdin, Y.
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A (2 + 1)-Dimensional Integrable Breaking Soliton Equation and Its Algebro-Geometric Solutions
MathematicsA new (2 + 1)-dimensional breaking soliton equation with the help of the nonisospectral Lax pair is presented. It is shown that the compatible solutions of the first two nontrivial equations in the (1 + 1)-dimensional Kaup–Newell soliton hierarchy ...
Xiaohong Chen +2 more
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General Solutions of the Abel Differential Equations
, 2020 The Abel differential equations play a significant role in various fields of mathematics and applied sciences and are classified into two types: the first kind and the second kind. A novel derivative condition for the general solution of first-kind Abel equation is introduced.
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Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations [PDF]
Physics Letters A, 2013 We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in its first kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative ...
Mancas, Stefan C., Rosu, Haret C.
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Electronic Journal of Qualitative Theory of Differential Equations, 2016 New and known properties of the resolvent of the kernel of linear Abel integral equations of the form \begin{equation} \tag{A$_\lambda$} x(t) = f(t) - \lambda \int_0^t (t - s)^{q-1}x(s)\,ds, \end{equation} where $\lambda > 0$ and $q \in (0,1)$, are ...
Leigh Becker
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Geometry of the Abel Equation of the first kind
, 2014 We study the first kind Abel differential equation $$\dfrac{dy}{dx}=c_0(x)+3c_1(x)y+3c_2y^2+c_3(x)y^3,$$ where the functions $c_i$ are real analytic. The first step of our analysis is through the Cartan equivalence method, then we use techniques from ...
Wone, Oumar
core
On centers for Generalized Abel Differential Equation
Journal of Zankoy Sulaimani - Part A, 2013 A new condition is given for generalized Abel differential equation to have a center. We apply the results to some polynomial differential systems in the plane to find necessary and sufficient center conditions.
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