# Painlevé Tests, Singularity Structure and Integrability

@article{Hone2009PainlevTS, title={Painlev{\'e} Tests, Singularity Structure and Integrability}, author={Andrew N W Hone}, journal={arXiv: Exactly Solvable and Integrable Systems}, year={2009}, pages={245-277} }

After a brief introduction to the Painleve property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painleve tests. The tests are applied to several different examples, and the connection between singularity structure and integrability of ordinary and partial differential equations is discussed.

## 53 Citations

### Singularity Analysis and Integrability of a Burgers-Type System of Foursov

- Mathematics
- 2011

We apply the Painleve test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess…

### Painlevé Test to a Reduced System of Six Coupled Nonlinear ODEs

- Mathematics
- 2010

Abstract: In this paper we investigate the complete integrability of the system of six coupled nonlinear ODEs, which arises in the ODE reduction of rotating stratified Boussinesq equations. We use…

### On Painlevé analysis for some non–linear evolution equations

- Mathematics
- 2014

In this paper, we present explicit Painlevé test for the potential Boussinesq equation, The murrary equation, The (2 + 1) Calogero equation, The Rosenau – Hyman equation (RH), Cole – Hopf (CH)…

### Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation

- MathematicsAdvances in Mathematical Physics
- 2021

In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield…

### The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source

- Mathematics
- 2012

The Painleve property and Backlund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painleve property.…

### Lax pair representation and Darboux transformation of NC Painlevé-II equation

- Mathematics
- 2012

The extension of Painleve equations to noncommutative spaces has been considering extensively in the theory of integrable systems and it is also interesting to explore some remarkable aspects of…

### On Integrability of Christouâ€™s Sixth Order Solitary Wave Equations

- MathematicsIraqi Journal of Science
- 2019

We examine the integrability in terms of PainlevÃ¨ analysis for several models of higher order nonlinear solitary wave equations which were recently derived by Christou. Our results point out that…

### Lax pair representation and Darboux transformation of noncommutative Painlevé’s second equation

- Mathematics
- 2012

### Integrability study of a four-dimensional eighth-order nonlinear wave equation

- Mathematics
- 2016

We study the integrability of the four-dimensional eighth-order nonlinear wave equation of Kac and Wakimoto, associated with the exceptional affine Lie algebra ${\mathfrak e}_6^{(1)}$. Using the…

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