The Painlevé handbook

By Robert Conte

Subjects: Differentiable dynamical systems, Equations, Physics, Chemistry, Mathematical physics, Painlevé equations, Mathematics, Differential Equations, Engineering mathematics, Partial Differential Equations, Dynamical Systems and Ergodic Theory, Appl.Mathematics/Computational Methods of Engineering, Math. Applications in Chemistry, Differential equations, partial, Mathematical Methods in Physics, Ordinary Differential Equations

Description: "This 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 many a priori knowledge of the solutions, with a powerful algorithm presented in detail called the Painleve test. If the equation under study passes the Painleve test, the equation is presumed integrable. If on the contrary the test fails, the system is nonintegrable of even chaotic, but it may still be possible to find solutions. Written at a graduate level, the book contains tutorial texts as well as detailed examples and the state of the art in some current research."--Jacket.