{"product_id":"9789401049245","title":"Applications of Analytic and Geometric Methods to Nonlinear Differential Equations","description":"\u003ch1\u003eApplications of Analytic and Geometric Methods to Nonlinear Differential Equations\u003c\/h1\u003e \u003ch2\u003eClarkson, P.A.\u003c\/h2\u003e \u003cp\u003eIn 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.\u003cbr\u003e  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.\u003cbr\u003e  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. Painlevé analysis of partial  differential equations, studies of the Painlevé equations and  symmetry reductions of nonlinear partial differential  equations.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e  (ABSTRACT)\u003cbr\u003e  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 severalarticles 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, Painlevé analysis of partial  differential equations, studies of the Painlevé equations and  symmetry reductions of nonlinear partial differential equations.\u003cbr\u003e\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-10-13\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9789401049245\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-94-011-2082-1\u003c\/p\u003e \u003cp\u003eDimensions: 240cm x160cm\u003c\/p\u003e \u003cp\u003ePages: 477\u003c\/p\u003e ","brand":"Springer","offers":[{"title":"Default Title","offer_id":44398522269836,"sku":"9789401049245","price":297.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9789401049245.jpg?v=1755436384","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9789401049245","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}