Results 1 to 10 of about 13,396 (146)
Planar nonautonomous polynomial equations V. The Abel equation [PDF]
Opuscula Mathematica, 2013 We give a full description of the dynamics of the Abel equation \(z'=z^3+f(t)\) for some special complex valued \(f\). We also prove the existence of at least three periodic solutions for equations of the form \(z'=z^n+f(t)\) for odd \(n \geq 5\).
Paweł Wilczyński
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Polynomial Solutions of Equivariant Polynomial Abel Differential Equations [PDF]
Advanced Nonlinear Studies, 2018 Let a(x){a(x)} be non-constant and let bj(x){b_{j}(x)}, for j=0,1,2,3{j=0,1,2,3}, be real or complex polynomials in the variable x. Then the real or complex equivariant polynomial Abel differential equation a(x)y˙=b1(x)y+b3(x)y3{a(x)\dot{y}=b_{1}(
Llibre Jaume, Valls Clàudia
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Rational Limit Cycles on Abel Polynomial Equations [PDF]
Mathematics, 2020 In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 .
Claudia Valls
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Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations [PDF]
Entropy, 2022 We apply the Simple Equations Method (SEsM) for obtaining exact travelling-wave solutions of the extended fifth-order Korteweg-de Vries (KdV) equation. We present the solution of this equation as a composite function of two functions of two independent ...
Elena V. Nikolova
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Nondegenerate centers for Abel polynomial differential equations of second kind [PDF]
Journal of Computational and Applied Mathematics, 2017 In this paper we study the center problem for Abel polynomial differential equations of second kind. Computing the focal values and using modular arithmetics and Gröbner bases we find the center conditions for such systems for lower degrees.The first ...
Giné, Jaume, Valls, Claudia
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Rational solutions and limit cycles of polynomial and trigonometric Abel equations
Electronic Journal of Qualitative Theory of Differential Equationse study the Abel differential equation $x'=A(t)x^3+B(t)x^2+C(t)x$. Specifically, we find bounds on the number of its rational solutions when $A(t), B(t)$ and $C(t)$ are polynomials with real or complex coefficients; and on the number of rational limit ...
Luis Ángel Calderón
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Electronic Journal of Differential Equations, 2017 Let $A(\theta)$ non-constant and $B_j(\theta)$ for $j=0,1,2,3$ be real trigonometric polynomials of degree at most $\eta \ge 1$ in the variable x. Then the real equivariant trigonometric polynomial Abel differential equations $A(\theta) y' =B_1(\theta)
Claudia Valls
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Algebro-Geometric Solutions of the Coupled Chaffee-Infante Reaction Diffusion Hierarchy
Advances in Mathematical Physics, 2021 The coupled Chaffee-Infante reaction diffusion (CCIRD) hierarchy associated with a 3×3 matrix spectral problem is derived by using two sets of the Lenard recursion gradients.
Chao Yue, Tiecheng Xia
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Solution of generalized Abel’s integral equation using orthogonal polynomials
Open Journal of Mathematical Analysis, 2022 This research presents the solution of the generalized version of Abel’s integral equation, which was computed considering the first and second kinds. First, Abel’s integral equation and its generalization were described using fractional calculus, and the properties of Orthogonal polynomials were also described.
Mamman Ojima John +2 more
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On Bernstein Polynomials Method to the System of Abel Integral Equations [PDF]
Abstract and Applied Analysis, 2014 This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem.
Ahmad Jafarian +3 more
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