Title Applications of Analytic and Geometric Methods to Nonlinear Differential Equations Author(s) Clarkson, P.A Publication Dordrecht, Springer Netherlands, 1993. Description X, 477 p : online resource Abstract Note In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years. (1) The inverse scattering transform (IST), using complex function theory, which has been employed to solve many physically significant equations, the `soliton' equations. (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 nonintegrable, and so asymptotic, numerical perturbation and reduction techniques are often used to study such equations. This book also contains articles on perturbed soliton equations. Painlev?? analysis of partial differential equations, studies of the Painlev?? equations and symmetry reductions of nonlinear partial differential equations. (ABSTRACT) In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years; the inverse scattering transform (IST), for `soliton' equations and twistor theory, for the self-dual Yang--Mills (SDYM) equations. This book contains several articles on the reduction of the SDYM equations to soliton equations and the relationship between the IST and twistor methods. Additionally, it contains articles on perturbed soliton equations, Painlev?? analysis of partial differential equations, studies of the Painlev?? equations and symmetry reductions of nonlinear partial differential equations ISBN,Price 9789401120821 Keyword(s) 1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. DIFFERENTIAL EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. ENGINEERING MATHEMATICS 7. GLOBAL ANALYSIS (MATHEMATICS) 8. Global Analysis and Analysis on Manifolds 9. Manifolds (Mathematics) 10. Mathematical and Computational Engineering 11. MATHEMATICAL PHYSICS 12. ORDINARY DIFFERENTIAL EQUATIONS 13. PARTIAL DIFFERENTIAL EQUATIONS 14. Theoretical, Mathematical and Computational Physics Item Type eBook Multi-Media Links Please Click here for eBook Circulation Data Accession#   Call# Status Issued To Return Due On Physical Location I02446     On Shelf