Results 1 to 10 of about 36,785 (158)
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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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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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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Abel fractional differential equations using Variation of parameters method
Ratio Mathematica, 2022 The Variation of Parameters Method (VPM) is utilized throughout the research to identify a numerical model for a nonlinear fractional Abel differential equation (FADE).
Nithya Devi, P. Prakash
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Universal Curves in the Center Problem for Abel Differential Equations [PDF]
Ergodic Theory and Dynamical Systems, 2014 We study the center problem for the class $\mathcal E_\Gamma$ of Abel differential equations $\frac{dv}{dt}=a_1 v^2+a_2 v^3$, $a_1,a_2\in L^\infty ([0,T])$, such that images of Lipschitz paths $\tilde A:=\bigl(\int_0^\cdot a_1(s)ds, \int_0^\cdot a_2(s)ds\
Brudnyi, Alexander
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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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Rational solutions of Abel differential equations
Journal of Mathematical Analysis and Applications, 2022 19 ...
J.L. Bravo +3 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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Advances in Mathematical Physics, 2022 The (2+1)-dimensional Lax integrable equation is decomposed into solvable ordinary differential equations with the help of known (1+1)-dimensional soliton equations associated with the Ablowitz-Kaup-Newell-Segur soliton hierarchy.
Xiaohong Chen
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Properties of inversion operator of the Abel matrix equation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010 Generalization of integral-differential Riemann-Liouville operator on the matrix order-is reviewed and its properties are studied. Theorem of the composition of operators of the matrix of integration and differentiation can be proved.
Rina R Ismagilova
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