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

• Autore: Kamvissis Spyridon
• 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
• 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
• Serie: Annals of mathematics studies ; ; no. 154.