LEADER 04650nam 2200697Ia 450 001 9910465228803321 005 20200520144314.0 010 $a1-299-44345-1 010 $a1-4008-3718-9 024 7 $a10.1515/9781400837182 035 $a(CKB)2560000000080613 035 $a(EBL)1163722 035 $a(OCoLC)845252685 035 $a(SSID)ssj0000508848 035 $a(PQKBManifestationID)12161422 035 $a(PQKBTitleCode)TC0000508848 035 $a(PQKBWorkID)10562646 035 $a(PQKB)10861435 035 $a(MiAaPQ)EBC1163722 035 $a(DE-B1597)446421 035 $a(OCoLC)979579304 035 $a(DE-B1597)9781400837182 035 $a(Au-PeEL)EBL1163722 035 $a(CaPaEBR)ebr10682501 035 $a(CaONFJC)MIL475595 035 $a(EXLCZ)992560000000080613 100 $a20030605d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSemiclassical soliton ensembles for the focusing nonlinear Schrodinger equation$b[electronic resource] /$fSpyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller 205 $aCourse Book 210 $aPrinceton, NJ $cPrinceton University Press$dc2003 215 $a1 online resource (280 p.) 225 1 $aAnnals of mathematics studies ;$vno. 154 300 $aDescription based upon print version of record. 311 $a0-691-11483-8 311 $a0-691-11482-X 320 $aIncludes bibliographical references (p. [255]-258) and index. 327 $tFrontmatter -- $tContents -- $tFigures and Tables -- $tPreface -- $tChapter 1. Introduction and Overview -- $tChapter 2. Holomorphic Riemann-Hilbert Problems for Solitons -- $tChapter 3. Semiclassical Soliton Ensembles -- $tChapter 4. Asymptotic Analysis of the Inverse Problem -- $tChapter 5. Direct Construction of the Complex Phase -- $tChapter 6. The Genus - Zero Ansatz -- $tChapter 7. The Transition to Genus Two -- $tChapter 8. Variational Theory of the Complex Phase -- $tChapter 9. Conclusion and Outlook -- $tAppendix A. H¨older Theory of Local Riemann-Hilbert Problems -- $tAppendix B. Near-Identity Riemann-Hilbert Problems in L2 -- $tBibliography -- $tIndex 330 $aThis book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe. To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis. 410 0$aAnnals of mathematics studies ;$vno. 154. 606 $aSchrodinger equation 606 $aWave mechanics 608 $aElectronic books. 615 0$aSchrodinger equation. 615 0$aWave mechanics. 676 $a530.12/4 686 $aSI 830$2rvk 700 $aKamvissis$b Spyridon$0150747 701 $aMcLaughlin$b K. T-R$g(Kenneth T-R),$f1969-$0150748 701 $aMiller$b Peter D$g(Peter David),$f1967-$0150749 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465228803321 996 $aSemiclassical soliton ensembles for the focusing nonlinear Schrodinger equation$92451282 997 $aUNINA