LEADER 08260nam 2201885Ia 450 001 9910822848003321 005 20230617011550.0 010 $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 610 $aAbelian integral. 610 $aAnalytic continuation. 610 $aAnalytic function. 610 $aAnsatz. 610 $aApproximation. 610 $aAsymptote. 610 $aAsymptotic analysis. 610 $aAsymptotic distribution. 610 $aAsymptotic expansion. 610 $aBanach algebra. 610 $aBasis (linear algebra). 610 $aBoundary (topology). 610 $aBoundary value problem. 610 $aBounded operator. 610 $aCalculation. 610 $aCauchy's integral formula. 610 $aCauchy's integral theorem. 610 $aCauchy's theorem (geometry). 610 $aCauchy?Riemann equations. 610 $aChange of variables. 610 $aCoefficient. 610 $aComplex plane. 610 $aCramer's rule. 610 $aDegeneracy (mathematics). 610 $aDerivative. 610 $aDiagram (category theory). 610 $aDifferentiable function. 610 $aDifferential equation. 610 $aDifferential operator. 610 $aDirac equation. 610 $aDisjoint union. 610 $aDivisor. 610 $aEigenfunction. 610 $aEigenvalues and eigenvectors. 610 $aElliptic integral. 610 $aEnergy minimization. 610 $aEquation. 610 $aEuler's formula. 610 $aEuler?Lagrange equation. 610 $aExistential quantification. 610 $aExplicit formulae (L-function). 610 $aFourier transform. 610 $aFredholm theory. 610 $aFunction (mathematics). 610 $aGauge theory. 610 $aHeteroclinic orbit. 610 $aHilbert transform. 610 $aIdentity matrix. 610 $aImplicit function theorem. 610 $aImplicit function. 610 $aInfimum and supremum. 610 $aInitial value problem. 610 $aIntegrable system. 610 $aIntegral curve. 610 $aIntegral equation. 610 $aInverse problem. 610 $aJacobian matrix and determinant. 610 $aKerr effect. 610 $aLaurent series. 610 $aLimit point. 610 $aLine (geometry). 610 $aLinear equation. 610 $aLinear space (geometry). 610 $aLogarithmic derivative. 610 $aLp space. 610 $aMinor (linear algebra). 610 $aMonotonic function. 610 $aNeumann series. 610 $aNormalization property (abstract rewriting). 610 $aNumerical integration. 610 $aOrdinary differential equation. 610 $aOrthogonal polynomials. 610 $aParameter. 610 $aParametrix. 610 $aParaxial approximation. 610 $aParity (mathematics). 610 $aPartial derivative. 610 $aPartial differential equation. 610 $aPerturbation theory (quantum mechanics). 610 $aPerturbation theory. 610 $aPole (complex analysis). 610 $aPolynomial. 610 $aProbability measure. 610 $aQuadratic differential. 610 $aQuadratic programming. 610 $aRadon?Nikodym theorem. 610 $aReflection coefficient. 610 $aRiemann surface. 610 $aSimultaneous equations. 610 $aSobolev space. 610 $aSoliton. 610 $aSpecial case. 610 $aTaylor series. 610 $aTheorem. 610 $aTheory. 610 $aTrace (linear algebra). 610 $aUpper half-plane. 610 $aVariational method (quantum mechanics). 610 $aVariational principle. 610 $aWKB approximation. 615 0$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 $a9910822848003321 996 $aSemiclassical soliton ensembles for the focusing nonlinear Schrodinger equation$93913605 997 $aUNINA