Conte R., Musette M. The Painlevé Handbook

Publisher: Springer; 1st edition (June 27, 2008), Hardcover: 256 pages, ISBN10: 1402084900 ISBN13: 978-1402084904This book introduces the reader to methods allowing one to build explicit solutions to these equations. A prerequisite task is to investigate whether the chances of success are high or low, and this can be achieved without any a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painlevé test. If the equation under study passes the Painlevé test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable or even chaotic, but it may still be possible to find solutions.