LEADER 03910nam 22006852 450 001 9910453833403321 005 20160525104242.0 010 $a1-107-19344-3 010 $a1-281-79136-9 010 $a9786611791360 010 $a0-511-42946-0 010 $a0-511-42827-8 010 $a0-511-42984-3 010 $a0-511-42766-2 010 $a0-511-54320-4 010 $a0-511-42898-7 035 $a(CKB)1000000000553012 035 $a(EBL)358851 035 $a(OCoLC)437222483 035 $a(SSID)ssj0000464429 035 $a(PQKBManifestationID)11319378 035 $a(PQKBTitleCode)TC0000464429 035 $a(PQKBWorkID)10420529 035 $a(PQKB)10350021 035 $a(UkCbUP)CR9780511543203 035 $a(MiAaPQ)EBC358851 035 $a(PPN)145865193 035 $a(Au-PeEL)EBL358851 035 $a(CaPaEBR)ebr10250535 035 $a(CaONFJC)MIL179136 035 $a(EXLCZ)991000000000553012 100 $a20090505d2008|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSoliton equations and their algebro-geometric solutions$hVolume 2$i(1 + 1)-dimensional discrete models /$fFritz Gesztesy [and three others]$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2008. 215 $a1 online resource (x, 438 pages) $cdigital, PDF file(s) 225 1 $aCambridge studies in advanced mathematics ;$v114 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-75308-2 320 $aIncludes bibliographical references and index. 327 $aCover; Half-title; Series-title; Title; Copyright; Contents; Acknowledgments; Introduction; 1 The Toda Hierarchy; 2 The Kac-van Moerbeke Hierarchy; 3 The Ablowitz-Ladik Hierarchy; Appendix A: Algebraic Curves and Their Theta Functions in a Nutshell; Appendix B: Hyperelliptic Curves of the Toda-Type; Appendix C: Asymptotic Spectral Parameter Expansions and Nonlinear Recursion Relations; Appendix D: Lagrange Interpolation; List of Symbols; Bibliography; Index; Errata and Addenda for Volume 330 $aAs a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appendices. Detailed notes for each chapter, together with an exhaustive bibliography, enhance understanding of the main results. 410 0$aCambridge studies in advanced mathematics ;$v114. 517 3 $aSoliton Equations & Their Algebro-Geometric Solutions 606 $aDifferential equations, Nonlinear$xNumerical solutions 606 $aSolitons 615 0$aDifferential equations, Nonlinear$xNumerical solutions. 615 0$aSolitons. 676 $a530.155355 700 $aGesztesy$b Fritz$f1953-$066693 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910453833403321 996 $aSoliton equations and their algebro-geometric solutions$91442406 997 $aUNINA