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Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller



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Autore: Kamvissis Spyridon Visualizza persona
Titolo: Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation [[electronic resource] /] / Spyridon Kamvissis, Kenneth D.T-R McLaughlin, Peter D. Miller Visualizza cluster
Pubblicazione: Princeton, NJ, : Princeton University Press, c2003
Edizione: Course Book
Descrizione fisica: 1 online resource (280 p.)
Disciplina: 530.12/4
Soggetto topico: Schrodinger equation
Wave mechanics
Soggetto non controllato: Abelian integral
Analytic continuation
Analytic function
Ansatz
Approximation
Asymptote
Asymptotic analysis
Asymptotic distribution
Asymptotic expansion
Banach algebra
Basis (linear algebra)
Boundary (topology)
Boundary value problem
Bounded operator
Calculation
Cauchy's integral formula
Cauchy's integral theorem
Cauchy's theorem (geometry)
Cauchy–Riemann equations
Change of variables
Coefficient
Complex plane
Cramer's rule
Degeneracy (mathematics)
Derivative
Diagram (category theory)
Differentiable function
Differential equation
Differential operator
Dirac equation
Disjoint union
Divisor
Eigenfunction
Eigenvalues and eigenvectors
Elliptic integral
Energy minimization
Equation
Euler's formula
Euler–Lagrange equation
Existential quantification
Explicit formulae (L-function)
Fourier transform
Fredholm theory
Function (mathematics)
Gauge theory
Heteroclinic orbit
Hilbert transform
Identity matrix
Implicit function theorem
Implicit function
Infimum and supremum
Initial value problem
Integrable system
Integral curve
Integral equation
Inverse problem
Jacobian matrix and determinant
Kerr effect
Laurent series
Limit point
Line (geometry)
Linear equation
Linear space (geometry)
Logarithmic derivative
Lp space
Minor (linear algebra)
Monotonic function
Neumann series
Normalization property (abstract rewriting)
Numerical integration
Ordinary differential equation
Orthogonal polynomials
Parameter
Parametrix
Paraxial approximation
Parity (mathematics)
Partial derivative
Partial differential equation
Perturbation theory (quantum mechanics)
Perturbation theory
Pole (complex analysis)
Polynomial
Probability measure
Quadratic differential
Quadratic programming
Radon–Nikodym theorem
Reflection coefficient
Riemann surface
Simultaneous equations
Sobolev space
Soliton
Special case
Taylor series
Theorem
Theory
Trace (linear algebra)
Upper half-plane
Variational method (quantum mechanics)
Variational principle
WKB approximation
Classificazione: SI 830
Altri autori: McLaughlinK. T-R <1969-> (Kenneth T-R)  
MillerPeter D <1967-> (Peter David)  
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (p. [255]-258) and index.
Nota di contenuto: Frontmatter -- Contents -- 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. H¨older Theory of Local Riemann-Hilbert Problems -- Appendix B. Near-Identity Riemann-Hilbert Problems in L2 -- Bibliography -- Index
Sommario/riassunto: This 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.
Titolo autorizzato: Semiclassical soliton ensembles for the focusing nonlinear Schrodinger equation  Visualizza cluster
ISBN: 1-299-44345-1
1-4008-3718-9
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910791959003321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; no. 154.