LEADER 03176nam 2200577 450 001 9910143967903321 005 20210210082627.0 010 $a3-540-77054-2 024 7 $a10.1007/978-3-540-77054-1 035 $a(CKB)1000000000546690 035 $a(SSID)ssj0000318337 035 $a(PQKBManifestationID)11249831 035 $a(PQKBTitleCode)TC0000318337 035 $a(PQKBWorkID)10308183 035 $a(PQKB)11100270 035 $a(DE-He213)978-3-540-77054-1 035 $a(MiAaPQ)EBC3063793 035 $a(MiAaPQ)EBC6350783 035 $a(PPN)13286133X 035 $a(EXLCZ)991000000000546690 100 $a20210210d2008 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntegrable hamiltonian hierarchies $espectral and geometric methods /$fV.S. Gerdjikov, G. Vilasi, A.B. Yanovski 205 $a1st ed. 2008. 210 1$aBerlin, Germany :$cSpringer,$d[2008] 210 4$dİ2008 215 $a1 online resource (XII, 643 p.) 225 1 $aLecture Notes in Physics,$x0075-8450 ;$v748 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-77053-4 320 $aIncludes bibliographical references and index. 327 $aIntegrable Hamiltonian Hierarchies: Spectral Methods -- The Lax Representation and the AKNS Approach -- The Direct Scattering Problem for theZakharov?Shabat System -- The Inverse Scattering Problem for the Zakharov?Shabat System -- The Generalized Fourier Transforms -- Fundamental Properties of the solvable NLEEs -- Hierarchies of Hamiltonian structures -- The NLEEs and the Gauge Transformations -- The Classical r-Matrix Method -- Integrable Hamiltonian Hierarchies: Geometric Theory of the Recursion Operators -- Smooth Manifolds -- Hamiltonian Dynamics -- Vector-Valued Differential Forms -- Integrability and Nijenhuis Tensors -- Poisson?Nijenhuis structures Related to the Generalized Zakharov?Shabat System -- Linear Bundles of Lie Algebras and Compatible Poisson Structures. 330 $aThis book presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their Hamiltonian hierarchies. Thus it is demonstrated that the inverse scattering method for solving soliton equations is a nonlinear generalization of the Fourier transform. The book brings together the spectral and the geometric approaches and as such will be useful to a wide readership: from researchers in the field of nonlinear completely integrable evolution equations to graduate and post-graduate students. 410 0$aLecture Notes in Physics,$x0075-8450 ;$v748 606 $aHamiltonian systems 615 0$aHamiltonian systems. 676 $a515.39 700 $aGerdjikov$b V. S$g(Vladimir Stefanov),$0602015 702 $aVilasi$b Gaetano 702 $aYanovski$b A. B$g(Alexandar Borissov), 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143967903321 996 $aIntegrable hamiltonian hierarchies$91016426 997 $aUNINA