Applications of Analytic and Geometric Methods to Nonlinear Differential Equations

Description

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.

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1. Ebooks list page : 3580
2. Functional Analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations
3. Methods of Nonlinear Analysis: Applications to Differential Equations
4. Variational Methods in Image Segmentation (Progress in Nonlinear Differential Equations and Their Applications, Vol 14)
5. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
6. Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems
7. Geometric Analysis and Nonlinear Partial Differential Equations
8. Partial Differential Equations Vol. 2: Functional Analytic Methods
9. Entire solutions of semilinear elliptic equations (Progress in Nonlinear Differential Equations and Their Applications)
10. Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications
11. Geometric Mechanics on Riemannian Manifolds: Applications to Partial Differential Equations
12. The Maximum Principle (Progress in Nonlinear Differential Equations and Their Applications)
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14. Analytic and Geometric Study of Stratified Spaces: Contributions to Analytic and Geometric Aspects
15. Decomposition Methods for Differential Equations: Theory and Applications
16. Applications of Symmetry Methods to Partial Differential Equations