# Symbolic Software for the Painlevé Test of Nonlinear Ordinary and Partial Differential Equations

@article{Baldwin2006SymbolicSF, title={Symbolic Software for the Painlev{\'e} Test of Nonlinear Ordinary and Partial Differential Equations}, author={Douglas Baldwin and Willy A. Hereman}, journal={Journal of Nonlinear Mathematical Physics}, year={2006}, volume={13}, pages={110 - 90} }

Abstract The automation of the traditional Painlevé test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of nonlinear ordinary and partial differential equations which may be parameterized by arbitrary functions (or constants). Except where limited by memory, there is no restriction on the number of independent or dependent variables. The package is quite robust in determining all the possible dominant behaviors of the Laurent series…

## 52 Citations

A note on the Painlevé test for nonlinear variable-coefficient PDEs

- MathematicsComput. Phys. Commun.
- 2009

Construction of exact partial solutions of nonintegrable systems by means of formal Laurent and Puiseux series

- MathematicsProgramming and Computer Software
- 2006

A package facilitating search for analytic solutions of nonintegrable systems of autonomous ordinary differential equations is suggested, which allows one to obtain single-valued and multivalued analytical solutions that were known to exist only in the form of formal Laurent and Puiseux series.

Painlevé Integrability of Nonlinear Schrödinger Equations with both Space- and Time-Dependent Coefficients

- Mathematics, Physics
- 2010

We investigate the Painleve integrability of nonautonomous nonlinear Schrodinger (NLS) equations with both space- and time-dependent dispersion, nonlinearity, and external potentials. The Painleve…

Painlevé test, complete symmetry classifications and exact solutions to R-D types of equations

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2021

A symbolic algorithm for computing recursion operators of nonlinear partial differential equations

- MathematicsInt. J. Comput. Math.
- 2010

A straightforward method for the symbolic computation of polynomial recursion operators of nonlinear PDEs in (1+1) dimensions is presented and the resulting symbolic package PDERecursionOperator.m can be used to test the complete integrability ofPolynomial PDE's that can be written as nonlinear evolution equations.

Painlevé integrability of a generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

- Mathematics, Physics
- 2013

By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painleve test for integrability…

Elliptic solutions of the quintic complex one-dimensional Ginzburg?Landau equation

- Mathematics
- 2007

The Conte–Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a prior restriction is to simplify calculations by means…

Exact and Numerical Solutions of Some Nonlinear Partial Differential Equations

- Mathematics
- 2014

v for coupled short plus equation. We derive the infinitesimals that admit the classical symmetry group. Five types arise depending on the nature of the Lie symmetry generator. In all types, we find…

Painlevé analysis for a new integrable equation combining the modified Calogero–Bogoyavlenskii–Schiff (MCBS) equation with its negative-order form

- Physics, Mathematics
- 2018

A new integrable equation is constructed by combining the recursion operator of the modified Calogero–Bogoyavlenskii–Schiff equation and its inverse recursion operator. The Painlevé is performed to…

Analysis on the Integrability of the Rayleigh-Plesset Equation with Painlev\'e Test and Lie Symmetry Groups

- Mathematics
- 2018

The Rayleigh-Plesset equation (RPE) is a nonlinear ordinary differential equation (ODE) of second order that governs the dynamics of a spherical bubble and plays an essential role in interpreting…

## References

SHOWING 1-10 OF 76 REFERENCES

Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple

- MathematicsComput. Phys. Commun.
- 2004

Implementation of the Painlevé Test for Ordinary Differential Systems

- MathematicsTheor. Comput. Sci.
- 1997

Algorithmic integrability tests for nonlinear differential and lattice equations

- Mathematics, Computer Science
- 1998

A constructive REDUCE package based upon the Painlevé analysis of nonlinear evolutions equations in Hamiltonian and / or normal form

- Mathematics
- 1992

A maple package for the Painleve Test of Nonlinear Partial Differential Equations

- Mathematics
- 2003

A Maple package,named PLtest,is presented to study whether or not nonlinear partial differential equations (PDEs) pass the Painleve test.This package is based on the so-called WTC-Kruskal…

A Maple Package for the Painlevé Test of Nonlinear Partial Differential Equations

- Mathematics
- 2003

A Maple package, named PLtest, is presented to study whether or not nonlinear partial differential equations (PDEs) pass the Painleve test. This package is based on the so-called WTC-Kruskal…

The Painlevé property for partial differential equations

- Mathematics
- 1983

In this paper we define the Painleve property for partial differential equations and show how it determines, in a remarkably simple manner, the integrability, the Backlund transforms, the linearizing…

PDEPtest: a package for the Painlevé test of nonlinear partial differential equations

- MathematicsAppl. Math. Comput.
- 2005

The Connection between Partial Differential Equations Soluble by Inverse Scattering and Ordinary Differential Equations of Painlevé Type

- Mathematics
- 1983

A completely integrable partial differential equation is one which has a Lax representation, or, more precisely, can be solved via a linear integral equation of Gel’fand–Levitan type, the classic…