Contemporary Mathematics 2002; 338 pp; softcover Volume: 301 ISBN10: 0821831615 ISBN13: 9780821831618 List Price: US$96 Member Price: US$76.80 Order Code: CONM/301
 Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as \(3\)wave resonant interactions and second harmonic generation, are becoming more and more relevant in experimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even more possibilities. This volume contains new developments and stateoftheart research arising from the conference on the "Legacy of the Inverse Scattering Transform" held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, "Reviews". This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects of solitontype equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multisoliton complexes, and on a unified approach to integrable systems via Painlevé analysis. This conference provided a forum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering. Readership Graduate students and researchers interested in mathematics, physics, and engineering. Reviews "More than a proceedings, this volume includes seven articles that review the state of research on different aspects of the field of solitons and the inverse scattering transform."  Book News, Inc. Table of Contents  D. J. Kaup  The legacy of the IST
 V. Zakharov  Application of inverse scattering method to problems of differential geometry
 V. S. Gerdjikov  Algebraic and analytic aspects of soliton type equations
 A. S. Fokas  Differential forms, spectral theory, and boundary value problems
 Y. C. Li  Chaos in partial differential equations
 N. N. Akhmediev, A. A. Sukhorukov, and A. Ankiewicz  Multisoliton complexes
 S. R. Choudhury  A unified approach to integrable systems via Painlevé analysis
 V. S. Buslaev and C. Sulem  Asymptotic stability of solitary waves for nonlinear Schrödinger equations
 A. de Bouard and A. Debussche  Finitetime blowup in the additive supercritical stochastic nonlinear Schrödinger equations: The real noise case
 O. I. Bogoyavlenskij  Method of symmetry transforms for ideal magnetohydrodynamics equilibrium equations
 R. Young  The \(p\)system I: The Riemann problem
 G. J. Morrow and S. Chakravarty  Statistical analysis of collisioninduced timing shifts in a wavelengthdivisionmultiplexed optical solitontransmission system
 R. Grimshaw, G. A. Gottwald, and B. A. Malomed  Cuspons and peakons visavis regular solitons and collapse in a threewave system
 S. Chakravarty and R. G. Halburd  First integrals and gradient flow for a generalized DarbouxHalphen system
 L. Casian and Y. Kodama  Blowups of the Toda lattices and their intersections with the Bruhat cells
 M. Kovalyov  Superposition principle for oscillatory solutions of integrable systems
 H. Steudel  Scattering at truncated solitons and inverse scattering on the semiline
