Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation
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A01=Kenneth D.T-R McLaughlin
A01=Kenneth Dean T-R McLaughlin
A01=Peter D. Miller
A01=Spyridon Kamvissis
Abelian integral
Analytic continuation
Analytic function
Ansatz
Approximation
Asymptote
Asymptotic analysis
Asymptotic distribution
Author_Kenneth D.T-R McLaughlin
Author_Kenneth Dean T-R McLaughlin
Author_Peter D. Miller
Author_Spyridon Kamvissis
Basis (linear algebra)
Boundary value problem
Bounded operator
Calculation
Category=PBK
Category=PHQ
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)
Diagram (category theory)
Differential equation
Differential operator
Dirac equation
Eigenfunction
Eigenvalues and eigenvectors
Elliptic integral
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
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Equation
Euler's formula
Euler-Lagrange equation
Existential quantification
Explicit formulae (L-function)
Fourier transform
Fredholm theory
Gauge theory
Heteroclinic orbit
Hilbert transform
Initial value problem
Integral curve
Integral equation
Inverse problem
Jacobian matrix and determinant
Line (geometry)
Linear equation
Logarithmic derivative
Minor (linear algebra)
Normalization property (abstract rewriting)
Ordinary differential equation
Parameter
Paraxial approximation
Partial derivative
Partial differential equation
Perturbation theory
Perturbation theory (quantum mechanics)
Pole (complex analysis)
Quadratic differential
Radon-Nikodym theorem
Reflection coefficient
Riemann surface
Simultaneous equations
Sobolev space
Soliton
Special case
Theorem
Theory
Upper half-plane
Variational method (quantum mechanics)
Variational principle
WKB approximation
Product details
- ISBN 9780691114828
- Weight: 454g
- Dimensions: 152 x 235mm
- Publication Date: 07 Sep 2003
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger 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 Holder 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.
Spyridon Kamvissis is a researcher at the Max Planck Institute of Mathematics in Bonn, Germany, and a Professor of Mathematics at the National Technical University in Athens, Greece. Kenneth D. T-R McLaughlin is Associate Professor of Mathematics at the University of North Carolina, Chapel Hill. Peter D. Miller is Assistant Professor of Mathematics at the University of Michigan, Ann Arbor.
