http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
1 online resource (xxvi, 810 pages) : illustrations.
The subject this volume is explicit integration, that is, the analytical as opposed to the numerical solution, of all kinds of nonlinear differential equations (ordinary differential, partial differential, finite difference). Such equations describe many physical phenomena, their analytic solutions (particular solutions, first integral, and so forth) are in many cases preferable to numerical computation, which may be long, costly and, worst, subject to numerical errors. In addition, the analytic approach can provide a global knowledge of the solution, while the numerical approach is always local. Explicit integration is based on the powerful methods based on an in-depth study of singularities, that were first used by Poincar and subsequently developed by Painlev in his famous Leons de Stockholm of 1895. The recent interest in the subject and in the equations investigated by Painlev dates back about thirty years ago, arising from three, apparently disjoint, fields: the Ising model of statistical physics and field theory, propagation of solitons, and dynamical systems. The chapters in this volume, based on courses given at Cargse 1998, alternate mathematics and physics; they are intended to bring researchers entering the field to the level of present research.
Singularities of Ordinary Linear Differential Equations -- Introduction to the Theory of Isomonodronic Deformations -- Painlev Approach to Nonlinear Ordinary Differential Equations -- Asymptotic Studies of the Painlev Equations -- 2D Quantum and Topological Gravities -- Painlev Transcendents in Two Dimensional Topological Field -- Discrete Painlev Equations -- Painlev Analysis for Partial Differential Equations -- On Painlev and Darboux Halpen Type Equations -- Symmetry Reduction and Exact Solutions -- Painlev Equations in Terms of Entire Functions -- Backlund Transformations of Painlev Equations -- The Hamiltonians Associated to Painleve Equations -- Completeness of the Painlev Test.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
Includes bibliographical references and index.