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.
• Monographs and Surveys in Pure and Applied Math
Differential Equations
Mathematics & Statistics for Engineers
Applied Mathematics
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In recent decades, the study of nonlinear integrable systems has grown into a full-fledged research topic. The ideas associated with Lie algebra and groups can form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author presents the techniques for using Lie algebraic concepts to explore nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as a tool. The text summarizes the use of these methods in various fields of theoretical research and serves mathematicians and theoretical physicists working in nonlinear integrable systems, dynamical systems, and chaos.
• Research Notes in Mathematics Series
Algebra
Mathematical Physics
Differential Equations
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Professional