Cover of: The nonlinear Schrödinger equation | C. Sulem

The nonlinear Schrödinger equation

self-focusing and wave collapse
  • 350 Pages
  • 1.51 MB
  • 6280 Downloads
by
Springer , New York
Schrödinger, Equation de, Schrödinger, Équation de, Schrödinger equation, Waves & Wave Mechanics, SCIENCE, Nonlinear theories, Théories non liné
StatementCatherine Sulem, Pierre-Louis Sulem
SeriesApplied mathematical sciences -- 139, Applied mathematical sciences (Springer-Verlag New York Inc.) -- v. 139.
ContributionsSulem, P. L.
Classifications
LC ClassificationsQC174.26.W28 S85 1999eb
The Physical Object
Format[electronic resource] :
Pagination1 online resource (xvi, 350 p.)
ID Numbers
Open LibraryOL27077651M
ISBN 100387227687
ISBN 139780387227689
OCLC/WorldCa53795457

Firstly, based on the small-signal analysis theory, the nonlinear Schrodinger equation (NLSE) with fiber loss is solved. It is also adapted to the NLSE with the high-order dispersion terms. Furthermore, a general theory on cross-phase modulation (XPM) intensity fluctuation which adapted to all kinds of modulation formats (continuous wave, non-return-to-zero wave, and return-zero pulse wave) is Cited by: 2.

“The Nonlinear Schrödinger Equation (NLS) theory was an object of great interest during last decades.

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the present book includes almost all questions connected with theoretical and experimental investigations of the above mentioned matter during the years since until now.

the book abounds in recent results, facts and examples that makes it very interesting for the researchers Cited by: This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation.

With great care and detail, it develops the subject including the mathematical and physical background and the history of the subject. This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource.

In addition, the book organizes the solutions by classifying and grouping them based on aspects and symmetries they possess. Although most of the solutions presented in this book have been derived elsewhere using various methods, the authors. The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Applied Mathematical Sciences) th Edition by Catherine Sulem (Author), Pierre-Louis Sulem (Author) out of 5 stars 2 ratings.

ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the Cited by: It contains the Matlab code for solving the generalized nonlinear Schrödinger equation given in Eq. () of Agrawal’s book on Nonlinear Fiber Optics (page 41 of the 6th edition published in ).

For better accuracy, this code uses the new form of the Raman response function given in Eq. () of this book. This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger : Gadi Fibich.

This book is an interdisciplinary introduction to optical collapse of laser beams, which is modelled by singular (blow-up) solutions of the nonlinear Schrödinger equation.

With great care and detail, it develops the subject including the mathematical and physical background and the history of theBrand: Springer International Publishing. T. Cazenave and F.

Weissler, The Cauchy problem for the nonlinear Schrödinger equation in H 1, Manuscripta Math. 61 (), – Google ScholarCited by:   From the mathematical point of view, Schrödinger's equation is a delicate problem, possessing a mixture of the properties of parabolic and elliptic equations.

Useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. This book collects all known solutions to the nonlinear Schrödinger equation (NLSE) in one resource. In addition, the book organizes the solutions by classifying and grouping them based on.

This book constitutes the first effort to summarize a large volume of results obtained over the past 20 years in the context of the Discrete Nonlinear Schrödinger equation and the physical settings that it describes. It contains an introduction to the model, its systematic derivation and its.

Description The nonlinear Schrödinger equation FB2

The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of by: You can find a detailed derivation of a nonlinear Schrödinger equation describing electromagnetic waves in such a medium in the book.

Ablowitz, B. Prinari, A. Trubatch: "Discrete and Continuous Nonlinear Schrödinger Systems", Cambridge University Press, The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schrödinger-type models that arise therein.

The Defocusing Nonlinear Schrödinger Equation is a broad study of nonlinear excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear.

This chapter provides a brief introduction to nonlinear optics by presenting a basic model for the nonlinear susceptibility, and shows how it is included to generalize the wave equation. Such an equation is used as the starting point to derive the central equation: the celebrated nonlinear Schrödinger equation (NLSE).

Multiple solutions for a fractional nonlinear Schrödinger equation with local potential. Communications on Pure & Applied Analysis,16 (6): Cited by: 8. This chapter provides a brief introduction to nonlinear optics by presenting a basic model for the nonlinear susceptibility, and shows how it is included to generalize the wave equation.

Such an equation is used as the starting point to derive the central equation: the celebrated nonlinear Schrödinger equation (NLSE). Buy The Nonlinear Schrödinger Equation Books online at best prices in India by Gadi Fibich from Buy The Nonlinear Schrödinger Equation online of India’s Largest Online Book Store, Only Genuine Products.

Lowest price and Replacement Guarantee. Cash On Delivery Available. The Schrödinger equation is a linear partial differential equation that describes the wave function or state function of a quantum-mechanical system.: 1–2 It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the equation is named after Erwin Schrödinger, who postulated the equation inand published it informing.

Get this from a library. Defocusing nonlinear Schrödinger equations. [Benjamin Dodson] -- This study of Schrödinger equations with power-type nonlinearity provides a great deal of insight into other dispersive partial differential equations and geometric partial differential equations.

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The system of coupled nonlinear Schrödinger equations (CNLSEs) also termed as the vector Schrödinger equation is a soliton supporting dynamical system. For the first time, it is considered as a model of light propagation in Kerr isotropic media (see, for example,).

Along with that, the phenomenology of the equation opens up the prospect of. Get this from a library. Global solutions of nonlinear Schrödinger equations. [Jean Bourgain] -- Presents recent progress in the theory of nonlinear dispersive equations, primarily the nonlinear Schrodinger (NLS) equation.

The Cauchy problem for defocusing NLS with critical nonlinearity is. Schrödinger equation, the fundamental equation of the science of submicroscopic phenomena known as quantum mechanics.

The equation, developed () by the Austrian physicist Erwin Schrödinger, has the same central importance to quantum mechanics as Newton’s laws of motion have for the large-scale phenomena of classical mechanics.

Pages from Volume (), Issue 1 by L. Hakan Eliasson, Sergei B. KuksinCited by:   The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation.

It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves. "The book contains various approaches to the Schrödinger equation (SE) as a fundamental equation of quantum mechanics.

In Chapter 1, a new pedagogical paradigm is proposed which allows one to understand quantum mechanics as an extension of probability theory; its purpose is providing alternative methods to understand the Schrödinger equation.

We introduce three sets of solutions to the nonlinear Schrödinger equation for the free particle case. A well-known solution is written in terms of Jacobi elliptic functions, which are the nonlinear versions of the trigonometric functions sin, cos, tan, cot, sec, and csc.

The nonlinear versions of the other related functions like the real and complex exponential functions and the linear Author: Gabino Torres Vega. The nonlinear Schrodinger equation (NLS) arises in many physical problems as an amplitude equation in nonlinear waves.

The main property that this chapter discusses is the equation's focusing singularity, that is, solutions of the equation that have a singularity at a finite by: 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 Range: $ - $. In this paper, we study the stability and the instability of standing waves for the nonlinear Schrödinger equation with harmonic potential.

We prove the existence of stable or unstable standing waves under certain conditions on the power of nonlinearity and the frequency of by: Semi-classical analysis for nonlinear Schrödinger equations / by: Carles, Rémi.

Published: () The discrete nonlinear Schrödinger equation mathematical analysis, numerical computations and physical perspectives / by: Kevrekidis, Panayotis G. Published: ().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.