Applications of Analytic and Geometric Methods to Nonlinear Differential Equations: 413 - Rilegato

 
9780792324577: Applications of Analytic and Geometric Methods to Nonlinear Differential Equations: 413

Sinossi

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past 20 years: 1. The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the "soliton" equations and 2. Twistor theory, using differential geometry, which has been used to solve the self-dual Yang-Mills (SDYM) equations, a four-dimensional system having important applications in mathematical physics. Both soliton and the SDYM equations have rich algebraic structures which have been extensively studied. Recently, it has been conjectured that, in some sense, all soliton equations arise as special cases of the SDYM equations. Subsequently many have been discovered as either exact or asymptotic reductions of the SDYM equations. Consequently what seems to be emerging is that a natural, physically significant system such as the SDYM equations provides the basis for a unifying framework underlying this class of integrable systems, i.e. "soliton" systems. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. The majority of nonlinear evolution equations are non-integrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations; Painleve analysis of partial differential equations; studies of the Painleve equations; and symmetry reductions of non-linear partial differential equations.

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Contenuti

Preface. I: Self-Dual Yang--Mills Equations. II: Completely Integrable Equations. III: Painlevé Equations and Painlevé Analysis. IV: Symmetries of Differential Equations. Author Index. Subject Index.

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9789401049245: Applications of Analytic and Geometric Methods to Nonlinear Differential Equations: (Closed)): 413

Edizione in evidenza

ISBN 10:  9401049246 ISBN 13:  9789401049245
Casa editrice: Springer, 2012
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