Direct and Inverse Methods in Nonlinear Evolution Equations Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5-12, 1999 /

• Main Authors: Conte, Robert M. (Author, http://id.loc.gov/vocabulary/relators/aut), Magri, Franco (http://id.loc.gov/vocabulary/relators/aut), Musette, Micheline (http://id.loc.gov/vocabulary/relators/aut), Satsuma, Junkichi (http://id.loc.gov/vocabulary/relators/aut), Winternitz, Pavel (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Other Authors: Greco, Antonio Maria (Editor, http://id.loc.gov/vocabulary/relators/edt)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Physics, 632
• Subjects: Physics.; Partial differential equations.; Differential geometry.; Statistical physics.; Dynamical systems.; Mathematical Methods in Physics.; Partial Differential Equations.; Differential Geometry.; Complex Systems.; Statistical Physics and Dynamical Systems.
• Physical Description: XI, 279 p. online resource.
• ISBN: 9783540398080
• ISSN: 0075-8450 ;
• DOI: 10.1007/b13714

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.