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| 001 | ocn839304452 | ||
| 003 | OCoLC | ||
| 005 | 20220711195348.0 | ||
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| 008 | 130415s2003 njua ob 001 0 eng d | ||
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| 049 | _aMAIN | ||
| 100 | 1 |
_aKamvissis, Spyridon. _9342886 |
|
| 245 | 1 | 0 |
_aSemiclassical soliton ensembles for the focusing nonlinear Schrödinger equation / _cSpyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller. |
| 260 |
_aPrinceton, N.J. : _bPrinceton University Press, _c©2003. |
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| 300 |
_a1 online resource (xii, 265 pages) : _billustrations |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 | _adata file | ||
| 380 | _aBibliography | ||
| 490 | 1 |
_aAnnals of mathematics studies ; _vno. 154 |
|
| 504 | _aIncludes bibliographical references (pages 255-258) and index. | ||
| 588 | 0 | _aPrint version record. | |
| 520 | _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. | ||
| 546 | _aIn English. | ||
| 505 | 0 | _aCover; Title; Copyright; Contents; List of Figures and Tables; Preface; Chapter 1. Introduction and Overview; Chapter 2. Holomorphic Riemann-Hilbert Problems for Solitons; Chapter 3. Semiclassical Soliton Ensembles; Chapter 4. Asymptotic Analysis of the Inverse Problem; Chapter 5. Direct Construction of the Complex Phase; Chapter 6. The Genus-Zero Ansatz; Chapter 7. The Transition to Genus Two; Chapter 8. Variational Theory of the Complex Phase; Chapter 9. Conclusion and Outlook; Appendix A. Hölder Theory of Local Riemann-Hilbert Problems | |
| 505 | 8 | _aAppendix B. Near-Identity Riemann-Hilbert Problems in L2Bibliography; Index | |
| 590 |
_aeBooks on EBSCOhost _bEBSCO eBook Subscription Academic Collection - Worldwide |
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| 650 | 0 |
_aSchrödinger equation. _9516753 |
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| 650 | 6 |
_aÉquation de Schrödinger. _9931180 |
|
| 650 | 7 |
_aSCIENCE _xWaves & Wave Mechanics. _2bisacsh _9872137 |
|
| 650 | 7 |
_aMATHEMATICS _xComplex Analysis. _2bisacsh _9904240 |
|
| 650 | 7 |
_aSchrödinger equation. _2fast _0(OCoLC)fst01108121 _9516753 |
|
| 650 | 7 |
_aNichtlineare Schrödinger-Gleichung _2gnd _9939546 |
|
| 650 | 7 |
_aSchrödinger-Gleichung _2gnd _9939547 |
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| 650 | 7 |
_aSoliton _2gnd _9900075 |
|
| 650 | 1 | 7 |
_aSchrödingervergelijking. _2gtt _9876861 |
| 650 | 1 | 7 |
_aSolitons. _2gtt _9145379 |
| 655 | 0 | _aElectronic books. | |
| 655 | 4 | _aElectronic books. | |
| 700 | 1 |
_aMcLaughlin, K. T-R _q(Kenneth T-R), _d1969- _9342888 |
|
| 700 | 1 |
_aMiller, Peter D. _q(Peter David), _d1967- _9342889 |
|
| 776 | 0 | 8 |
_iPrint version: _aKamvissis, Spyridon. _tSemiclassical soliton ensembles for the focusing nonlinear Schrödinger equation. _dPrinceton, N.J. : Princeton University Press, ©2003 _z0691114838 _w(DLC) 2003108056 _w(OCoLC)51780336 |
| 830 | 0 |
_aAnnals of mathematics studies ; _vno. 154. _9215873 |
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