Direct and Inverse Methods in Nonlinear Evolution Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Direct and Inverse Methods in Nonlinear Evolution Equations write by Robert M. Conte. This book was released on 2003-10-21. Direct and Inverse Methods in Nonlinear Evolution Equations available in PDF, EPUB and Kindle. Many physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved.
Inverse Problems and Nonlinear Evolution Equations
Inverse Problems and Nonlinear Evolution Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Inverse Problems and Nonlinear Evolution Equations write by Alexander L. Sakhnovich. This book was released on 2013-07-31. Inverse Problems and Nonlinear Evolution Equations available in PDF, EPUB and Kindle. This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.
Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications
Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications write by Robert M. Miura. This book was released on 2006-11-14. Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications available in PDF, EPUB and Kindle. Proceedings of the NSF Research Workshop on Contact Transformations, Held in Nashville, Tennessee, 1974
Optimal Transportation and Applications
Optimal Transportation and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Optimal Transportation and Applications write by Luigi Ambrosio. This book was released on 2003-06-12. Optimal Transportation and Applications available in PDF, EPUB and Kindle. Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory.
The Global Theory of Minimal Surfaces in Flat Spaces
The Global Theory of Minimal Surfaces in Flat Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Global Theory of Minimal Surfaces in Flat Spaces write by W.H. III Meeks. This book was released on 2004-10-11. The Global Theory of Minimal Surfaces in Flat Spaces available in PDF, EPUB and Kindle. In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.
