LEADER 05115nam 22006854a 450 001 9910782287503321 005 20200520144314.0 010 $a1-281-93445-3 010 $a9786611934453 010 $a981-279-451-4 035 $a(CKB)1000000000537855 035 $a(EBL)1679287 035 $a(OCoLC)879023409 035 $a(SSID)ssj0000248467 035 $a(PQKBManifestationID)11210072 035 $a(PQKBTitleCode)TC0000248467 035 $a(PQKBWorkID)10201733 035 $a(PQKB)10746621 035 $a(MiAaPQ)EBC1679287 035 $a(WSP)00005108 035 $a(Au-PeEL)EBL1679287 035 $a(CaPaEBR)ebr10255609 035 $a(CaONFJC)MIL193445 035 $a(PPN)164380469 035 $a(EXLCZ)991000000000537855 100 $a20020911d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSoliton equations and Hamiltonian systems$b[electronic resource] /$fL.A. Dickey 205 $a2nd ed. 210 $aRiver Edge, NJ $cWorld Scientific$dc2003 215 $a1 online resource (421 p.) 225 1 $aAdvanced series in mathematical physics ;$vv. 26 300 $aDescription based upon print version of record. 311 $a981-238-173-2 320 $aIncludes bibliographical references. 327 $aContents ; Preface to the Second Edition ; Introduction to the First Edition ; Chapter 1 Integrable Systems Generated by Linear Differential nth Order Operators ; 1.1 Differential Algebra A ; 1.2 Space of Functionals A ; 1.3 Ring of Pseudodifferential Operators 327 $a1.4 Lax Pairs. GD Hierarchies of Equations 1.5 First Integrals (Constants of Motion) ; 1.6 Compatibility of the Equations of a Hierarchy ; 1.7 Soliton Solutions ; 1.8 Resolvent. Adler Mapping ; Chapter 2 Hamiltonian Structures ; 2.1 Finite-Dimensional Case ; 2.2 Hamilton Mapping 327 $a2.3 Variational Principles 2.4 Symplectic Form on an Orbit of the Coadjoint Representation of a Lie Group ; 2.5 Purely Algebraic Treatment of the Hamiltonian Structure ; 2.6 Examples ; Chapter 3 Hamiltonian Structure of the GD Hierarchies ; 3.1 Lie Algebra V Dual Space Q1 and Module Q0 327 $a3.2 Proof of Theorem 3.1.2 3.3 Poisson Bracket ; 3.4 Reduction to the Submanifold Un-1 = 0 ; 3.5 Variational Derivative of the Resolvent ; 3.6 Hamiltonians of the GD Hierarchies ; 3.7 Theory of the KdV-Hierarchy (n = 2) Independent of the General Case 327 $aChapter 4 Modified KdV and GD. The Kupershmidt-Wilson Theorem 4 1 Miura Transformation. The Kupershmidt-Wilson Theorem ; 4.2 Modified KdV Equation. Backlund Transformations ; 4.3 More on Modified GD Equations ; Chapter 5 The KP Hierarchy ; 5.1 Definition of the KP Hierarchy 327 $a5.2 Reduction of the KP Hierarchy to GD 330 $a The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also bec 410 0$aAdvanced series in mathematical physics ;$vv. 26. 606 $aSolitons 606 $aHamiltonian systems 615 0$aSolitons. 615 0$aHamiltonian systems. 676 $a530.12/4 700 $aDickey$b Leonid A$042685 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782287503321 996 $aSoliton equations and hamiltonian systems$9191382 997 $aUNINA