
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 selfdual YangMills (SDYM) equations, a fourdimensional 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 selfdual YangMills (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 
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