Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154)
()
About this ebook
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.
Related to Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154)
Titles in the series (100)
A Theory of Cross-Spaces. (AM-26), Volume 26 Rating: 0 out of 5 stars0 ratingsThe Two-Valued Iterative Systems of Mathematical Logic. (AM-5), Volume 5 Rating: 0 out of 5 stars0 ratingsDegree of Approximation by Polynomials in the Complex Domain. (AM-9), Volume 9 Rating: 0 out of 5 stars0 ratingsConvergence and Uniformity in Topology. (AM-2), Volume 2 Rating: 0 out of 5 stars0 ratingsAlgebraic Theory of Numbers. (AM-1), Volume 1 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-20), Volume I Rating: 0 out of 5 stars0 ratingsLectures on Differential Equations. (AM-14), Volume 14 Rating: 0 out of 5 stars0 ratingsAn Introduction to Linear Transformations in Hilbert Space. (AM-4), Volume 4 Rating: 0 out of 5 stars0 ratingsMetric Methods of Finsler Spaces and in the Foundations of Geometry. (AM-8) Rating: 0 out of 5 stars0 ratingsAutomata Studies. (AM-34), Volume 34 Rating: 5 out of 5 stars5/5The Calculi of Lambda-Conversion (AM-6), Volume 6 Rating: 4 out of 5 stars4/5Consistency of the Continuum Hypothesis. (AM-3), Volume 3 Rating: 0 out of 5 stars0 ratingsFinite Dimensional Vector Spaces. (AM-7), Volume 7 Rating: 4 out of 5 stars4/5Topics in Topology. (AM-10), Volume 10 Rating: 0 out of 5 stars0 ratingsProbleme General de la Stabilite du Mouvement. (AM-17), Volume 17 Rating: 0 out of 5 stars0 ratingsIntroduction to Non-Linear Mechanics. (AM-11), Volume 11 Rating: 0 out of 5 stars0 ratingsTopological Methods in the Theory of Functions of a Complex Variable. (AM-15), Volume 15 Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-45), Volume V Rating: 0 out of 5 stars0 ratingsTranscendental Numbers. (AM-16) Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-24), Volume I Rating: 0 out of 5 stars0 ratingsFunctional Operators (AM-22), Volume 2: The Geometry of Orthogonal Spaces. (AM-22) Rating: 0 out of 5 stars0 ratingsExistence Theorems in Partial Differential Equations. (AM-23), Volume 23 Rating: 0 out of 5 stars0 ratingsOrder-Preserving Maps and Integration Processes. (AM-31), Volume 31 Rating: 0 out of 5 stars0 ratingsMeromorphic Functions and Analytic Curves. (AM-12) Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Nonlinear Oscillations (AM-29), Volume II Rating: 0 out of 5 stars0 ratingsCurvature and Betti Numbers. (AM-32), Volume 32 Rating: 0 out of 5 stars0 ratingsAn Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18 Rating: 0 out of 5 stars0 ratingsContributions to Fourier Analysis. (AM-25) Rating: 0 out of 5 stars0 ratingsContributions to the Theory of Games (AM-39), Volume III Rating: 0 out of 5 stars0 ratingsLectures on the Theory of Games (AM-37) Rating: 1 out of 5 stars1/5
Related ebooks
Discrete Orthogonal Polynomials. (AM-164): Asymptotics and Applications (AM-164) Rating: 0 out of 5 stars0 ratingsWave Scattering by Time-Dependent Perturbations: An Introduction Rating: 5 out of 5 stars5/5The Standard Model in a Nutshell Rating: 0 out of 5 stars0 ratingsThe Hypoelliptic Laplacian and Ray-Singer Metrics. (AM-167) Rating: 0 out of 5 stars0 ratingsComputational Electromagnetism: Variational Formulations, Complementarity, Edge Elements Rating: 0 out of 5 stars0 ratingsIntroduction to Wave Scattering, Localization, and Mesoscopic Phenomena Rating: 0 out of 5 stars0 ratingsFinancial Derivatives in Theory and Practice Rating: 4 out of 5 stars4/5Scattering of Electromagnetic Waves: Numerical Simulations Rating: 0 out of 5 stars0 ratingsNotes on Elementary Particle Physics Rating: 0 out of 5 stars0 ratingsTheory of Fully Ionized Plasmas Rating: 0 out of 5 stars0 ratingsAtomic Collisions and Spectra Rating: 0 out of 5 stars0 ratingsModern Astrodynamics: Fundamentals and Perturbation Methods Rating: 0 out of 5 stars0 ratingsLectures on the Infrared Structure of Gravity and Gauge Theory Rating: 0 out of 5 stars0 ratingsThe Semiclassical Way to Dynamics and Spectroscopy Rating: 0 out of 5 stars0 ratingsCausality and Dispersion Relations Rating: 0 out of 5 stars0 ratingsCondensed Matter in a Nutshell Rating: 5 out of 5 stars5/5Particle Physics: An Introduction Rating: 4 out of 5 stars4/5Introduction to Elementary Particle Theory: International Series of Monographs In Natural Philosophy Rating: 0 out of 5 stars0 ratingsLectures in Scattering Theory: International Series of Monographs in Natural Philosophy Rating: 0 out of 5 stars0 ratingsLambda-Matrices and Vibrating Systems Rating: 3 out of 5 stars3/5Theory and Design of Broadband Matching Networks: Applied Electricity and Electronics Rating: 0 out of 5 stars0 ratingsElectromagnetic Processes Rating: 0 out of 5 stars0 ratingsPrinceton Guide to Advanced Physics Rating: 5 out of 5 stars5/5Data Analysis for Scientists and Engineers Rating: 0 out of 5 stars0 ratingsRays, Waves, and Scattering: Topics in Classical Mathematical Physics Rating: 0 out of 5 stars0 ratingsProbability Methods for Approximations in Stochastic Control and for Elliptic Equations Rating: 0 out of 5 stars0 ratingsCoupled-Oscillator Based Active-Array Antennas Rating: 0 out of 5 stars0 ratingsScattering, Natural Surfaces, and Fractals Rating: 4 out of 5 stars4/5Random Matrices: Revised and Enlarged Second Edition Rating: 0 out of 5 stars0 ratingsActive Galactic Nuclei: From the Central Black Hole to the Galactic Environment Rating: 0 out of 5 stars0 ratings
Mathematics For You
Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5Calculus For Dummies Rating: 4 out of 5 stars4/5Algebra - The Very Basics Rating: 5 out of 5 stars5/5Geometry For Dummies Rating: 5 out of 5 stars5/5Basic Math Notes Rating: 5 out of 5 stars5/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5Algebra I Workbook For Dummies Rating: 3 out of 5 stars3/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5Mental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5Calculus Made Easy Rating: 4 out of 5 stars4/5The Elements of Euclid for the Use of Schools and Colleges (Illustrated) Rating: 0 out of 5 stars0 ratingsThe Golden Ratio: The Divine Beauty of Mathematics Rating: 5 out of 5 stars5/5Is God a Mathematician? Rating: 4 out of 5 stars4/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5The Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsRelativity: The special and the general theory Rating: 5 out of 5 stars5/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5GED® Math Test Tutor, 2nd Edition Rating: 0 out of 5 stars0 ratingsAlgebra I For Dummies Rating: 4 out of 5 stars4/5
Reviews for Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM-154)
0 ratings0 reviews