scholarly journals THE NUMBER OF RATIONAL SOLUTIONS OF ABEL EQUATIONS

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Xinjie Qian ◽  
◽  
Yang Shen ◽  
Jiazhong Yang ◽  
Keyword(s):  
Rational Solutions ◽  
Abel Equations

Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
M. J. Álvarez ◽  
J. L. Bravo ◽  
M. Fernández ◽  
R. Prohens
Keyword(s):  
Limit Cycles ◽  
Abel Equations

scholarly journals ON PROPERTIES OF FINITE-ORDER MEROMORPHIC SOLUTIONS OF A CERTAIN DIFFERENCE PAINLEVÉ I EQUATION

2011 ◽  
Vol 85 (3) ◽  
pp. 463-475 ◽  
Author(s):  
MEI-RU CHEN ◽  
ZONG-XUAN CHEN
Keyword(s):  
Finite Order ◽  
Meromorphic Solutions ◽  
Rational Solutions ◽  
Polynomial Solutions ◽  
The Difference ◽  
Image Position

AbstractIn this paper, we investigate properties of finite-order transcendental meromorphic solutions, rational solutions and polynomial solutions of the difference Painlevé I equation where a, b and c are constants, ∣a∣+∣b∣≠0.

On the rational limit cycles of Abel equations

2018 ◽  
Vol 110 ◽  
pp. 28-32 ◽  
Author(s):  
Changjian Liu ◽  
Chunhui Li ◽  
Xishun Wang ◽  
Junqiao Wu
Keyword(s):  
Limit Cycles ◽  
Abel Equations

Rational solutions of the KdV equation with damping

1979 ◽  
Vol 24 (4) ◽  
pp. 97-100 ◽  
Author(s):  
F. Calogero ◽  
M. A. Olshanetsky ◽  
A. M. Perelomov
Keyword(s):  
Kdv Equation ◽  
Rational Solutions ◽  
The Kdv Equation

RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION

2008 ◽  
Vol 06 (04) ◽  
pp. 349-369 ◽  
Author(s):  
PETER A. CLARKSON
Keyword(s):  
Infinite Number ◽  
Boussinesq Equation ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Rational Solutions ◽  
Painleve Equations ◽  
Special Polynomials ◽  
Symmetry Reductions ◽  
Nonlinear Schrodinger Equations ◽  
De Vries

Rational solutions of the Boussinesq equation are expressed in terms of special polynomials associated with rational solutions of the second and fourth Painlevé equations, which arise as symmetry reductions of the Boussinesq equation. Further generalized rational solutions of the Boussinesq equation, which involve an infinite number of arbitrary constants, are derived. The generalized rational solutions are analogs of such solutions for the Korteweg–de Vries and nonlinear Schrödinger equations.

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