Painleve tests, singularity structure and integrability

Details Painleve tests, singularity structure and integrability Painleve tests, singularity structure and integrability

2005-02-09

arxiv.org/abs/nlin/0502017v2

Springer Lect. Notes Phys. 767 (2009) 245-277

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Final version appears as Chapter 7 in Integrability, A.V. Mikhailov (ed.), Springer (2009)

Scientific paper

After a brief introduction to the Painlev\'{e} property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painlev\'{e} tests. The tests are applied to several different examples, and we discuss the connection between singularity structure and integrability for ordinary and partial differential equations.

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