Painleve Analysis and Its Applications

With interest in the study of nonlinear systems at an all-time high, researchers are eager to explore the mysteries behind the nonlinear equations that govern various physical processes. Painleve analysis may be the only tool available that allows the analysis of both integrable and non-integrable systems. With a primary objective of introducing the uninitiated to the various techniques of the Painleve approach, this monograph brings together the results of the extensive research performed in the field over the last few decades. For the first time in a single volume, this book offers treatment of both the theory of Painleve analysis and its practical applications. In it, the author addresses the soliton and nonlinearity, Painleve analysis and the integrability of ordinary and partial differential equations, Painleve properties, different forms of expansion, and the relation of Painleve expansion with conformal invariance. He also gives a detailed account of negative resonances, explains the connection with monodromy, and demonstrates applications to specific important equations. Painleve Analysis and Its Applications offers a clear presentation and down-to-earth approach that includes many examples and requires only a basic understanding of complex function theory and differential equations.