LEADER 04651nam 22007335 450 001 9910257386303321 005 20200701204451.0 010 $a3-540-39808-2 024 7 $a10.1007/b13714 035 $a(CKB)1000000000230817 035 $a(SSID)ssj0000322642 035 $a(PQKBManifestationID)11247836 035 $a(PQKBTitleCode)TC0000322642 035 $a(PQKBWorkID)10305705 035 $a(PQKB)10867442 035 $a(DE-He213)978-3-540-39808-0 035 $a(EXLCZ)991000000000230817 100 $a20150519d2003 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aDirect and Inverse Methods in Nonlinear Evolution Equations$b[electronic resource] $eLectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 5?12, 1999 /$fby Robert M. Conte, Franco Magri, Micheline Musette, Junkichi Satsuma, Pavel Winternitz ; edited by Antonio Maria Greco 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (XI, 279 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v632 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-20087-8 327 $aExact 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. 330 $aMany physical phenomena are described by nonlinear evolution equation. Those that are integrable provide various mathematical methods, presented by experts in this tutorial book, to find special analytic solutions to both integrable and partially integrable equations. The direct method to build solutions includes the analysis of singularities à la Painlevé, Lie symmetries leaving the equation invariant, extension of the Hirota method, construction of the nonlinear superposition formula. The main inverse method described here relies on the bi-hamiltonian structure of integrable equations. The book also presents some extension to equations with discrete independent and dependent variables. The different chapters face from different points of view the theory of exact solutions and of the complete integrability of nonlinear evolution equations. Several examples and applications to concrete problems allow the reader to experience directly the power of the different machineries involved. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v632 606 $aPhysics 606 $aPartial differential equations 606 $aDifferential geometry 606 $aStatistical physics 606 $aDynamical systems 606 $aMathematical Methods in Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19013 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aPhysics. 615 0$aPartial differential equations. 615 0$aDifferential geometry. 615 0$aStatistical physics. 615 0$aDynamical systems. 615 14$aMathematical Methods in Physics. 615 24$aPartial Differential Equations. 615 24$aDifferential Geometry. 615 24$aComplex Systems. 615 24$aStatistical Physics and Dynamical Systems. 676 $a530.15/5353 700 $aConte$b Robert M$4aut$4http://id.loc.gov/vocabulary/relators/aut$01058466 702 $aMagri$b Franco$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMusette$b Micheline$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSatsuma$b Junkichi$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWinternitz$b Pavel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGreco$b Antonio Maria$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a9910257386303321 996 $aDirect and Inverse Methods in Nonlinear Evolution Equations$92500005 997 $aUNINA