000 03186nam a22005415i 4500
001 978-3-540-77054-1
003 DE-He213
005 20160302163654.0
007 cr nn 008mamaa
008 100301s2008 gw | s |||| 0|eng d
020 _a9783540770541
_9978-3-540-77054-1
024 7 _a10.1007/978-3-540-77054-1
_2doi
050 4 _aQC5.53
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
082 0 4 _a530.15
_223
245 1 0 _aIntegrable Hamiltonian Hierarchies
_h[electronic resource] :
_bSpectral and Geometric Methods /
_cedited by V.S. Gerdjikov, G. Vilasi, A.B. Yanovski.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXII, 643 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v748
505 0 _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.
520 _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.
650 0 _aPhysics.
650 0 _aMathematical analysis.
650 0 _aAnalysis (Mathematics).
650 0 _aGeometry.
650 1 4 _aPhysics.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aAnalysis.
650 2 4 _aTheoretical, Mathematical and Computational Physics.
650 2 4 _aGeometry.
650 2 4 _aPhysics, general.
700 1 _aGerdjikov, V.S.
_eeditor.
700 1 _aVilasi, G.
_eeditor.
700 1 _aYanovski, A.B.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540770534
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v748
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-540-77054-1
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c181876
_d181876