The Painlevé property for partial differential equations

1983 ◽  
Vol 24 (3) ◽  
pp. 522-526 ◽  
Author(s):  
John Weiss ◽  
M. Tabor ◽  
George Carnevale
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Painlevé Property

scholarly journals Integrability of Differential Equations with Fluid Mechanics Application: from Painleve Property to the Method of Simplest Equation

2013 ◽  
Vol 43 (2) ◽  
pp. 31-42 ◽  
Author(s):  
Zlatinka I. Dimitrova ◽  
Kaloyan N. Vitanov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fluid Mechanics ◽  
Exact Solutions ◽  
Inverse Scattering ◽  
Nonlinear Pde ◽  
Partial Differential ◽  
Modified Method ◽  
Painlevé Property ◽  
Linear Pdes

Abstract We present a brief overview of integrability of nonlinear ordinary and partial differential equations with a focus on the Painleve property: an ODE of second order possesses the Painleve property if the only movable singularities connected to this equation are single poles. The importance of this property can be seen from the Ablowitz-Ramani- Segur conhecture that states that a nonlinear PDE is solvable by inverse scattering transformation only if each nonlinear ODE obtained by ex- act reduction of this PDE possesses the Painleve property. The Painleve property motivated much research on obtaining exact solutions on non- linear PDEs and leaded in particular to the method of simplest equation. A version of this method called modified method of simplest equation is discussed below.

Sign in / Sign up

Export Citation Format

Share Document