04649nam 22007335 450 99646682760331620200701204451.03-540-39808-210.1007/b13714(CKB)1000000000230817(SSID)ssj0000322642(PQKBManifestationID)11247836(PQKBTitleCode)TC0000322642(PQKBWorkID)10305705(PQKB)10867442(DE-He213)978-3-540-39808-0(EXLCZ)99100000000023081720150519d2003 u| 0engurnn#008mamaatxtccrDirect and Inverse Methods in Nonlinear Evolution Equations[electronic resource] Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5–12, 1999 /by Robert M. Conte, Franco Magri, Micheline Musette, Junkichi Satsuma, Pavel Winternitz ; edited by Antonio Maria Greco1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (XI, 279 p.)Lecture Notes in Physics,0075-8450 ;632Bibliographic Level Mode of Issuance: Monograph3-540-20087-8 Exact Solutions of Nonlinear Partial Differential Equations by Singularity Analysis -- The Method of Poisson Pairs in the Theory of Nonlinear PDEs -- Nonlinear Superposition Formulae of Integrable Partial Differential Equations by the Singular Manifold Method -- Hirota Bilinear Method for Nonlinear Evolution Equations -- Lie Groups, Singularities and Solutions of Nonlinear Partial Differential Equations.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.Lecture Notes in Physics,0075-8450 ;632PhysicsPartial differential equationsDifferential geometryStatistical physicsDynamical systemsMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Differential Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21022Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Statistical Physics and Dynamical Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P19090Physics.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.530.15/5353Conte Robert Mauthttp://id.loc.gov/vocabulary/relators/aut1058466Magri Francoauthttp://id.loc.gov/vocabulary/relators/autMusette Michelineauthttp://id.loc.gov/vocabulary/relators/autSatsuma Junkichiauthttp://id.loc.gov/vocabulary/relators/autWinternitz Pavelauthttp://id.loc.gov/vocabulary/relators/autGreco Antonio Mariaedthttp://id.loc.gov/vocabulary/relators/edtBOOK996466827603316Direct and Inverse Methods in Nonlinear Evolution Equations2500005UNISA