Last edited by Zulusida
Wednesday, August 5, 2020 | History

12 edition of Korteweg-de Vries and Nonlinear Schrödinger Equations found in the catalog.

# Korteweg-de Vries and Nonlinear Schrödinger Equations

## by Peter E. Zhidkov

Written in English

Subjects:
• Differential Equations,
• Integral Equations,
• Partial Differential Equations,
• Mathematics,
• Science/Mathematics,
• Differential Equations - Partial Differential Equations,
• General,
• Mathematical Physics,
• Mathematics / Differential Equations,
• Well-posedness,
• invariant measure,
• stability,
• stationary solution,
• Mathematical Analysis,
• Korteweg-de Vries equation,
• Schrodinger equation,
• Schrèodinger equation

• The Physical Object
FormatPaperback
Number of Pages147
ID Numbers
Open LibraryOL12774710M
ISBN 103540418334
ISBN 109783540418337

We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled Book Search tips Selecting this option will search all publications across the Scitation platform and Z. N. Zhu, “ Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation,” J. Math. Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrödinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in.

di erential equations. The rst system is composed by a nonlinear Schr odinger equation and a Korteweg-de Vries equation as follows ˆ if t+ f xx+ jfj2f+ fg = 0 g t+ g xxx+ gg x+ 1 2 2(jfj) x = 0; (S1) where f = f(x;t) 2C while g = g(x;t) 2R, and 2R is the real coupling coe cient. System (S1) appears in phenomena of interactions between short and. Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory Author: Peter E. Zhidkov Published by Springer Berlin Heidelberg ISBN: DOI: / Table of Contents: Introduction Notation Evolutionary equations. Results on existence Stationary problems Stability of solutions Invariant measures.

The book gives thorough coverage of the derivation and solution methods for all fundamental nonlinear model equations, such as Korteweg-de Vries, Camassa-Holm, Degasperis-Procesi, Euler-Poincaré, Toda lattice, Boussinesq, Burgers, Fisher, Whitham, nonlinear Klein-Gordon, sine-Gordon, nonlinear Schrödinger, nonlinear reaction-diffusion, and. Linear Wave Equations. Traveling Wave and Soliton Solutions. A Linear Advective, Nonlinear Reaction Equation. Burgers' Equation. The Fisher Equation. The Korteweg-de Vries Equation. The Nonlinear Schrödinger Equation. Similarity Methods and Solutions. Similarity Methods. Examples. The Boltzmann Problem. The Nonlinear Diffusion Equation: uu t.

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### Korteweg-de Vries and Nonlinear Schrödinger Equations by Peter E. Zhidkov Download PDF EPUB FB2

Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory. Authors (view affiliations) Peter E. Zhidkov; Book. About this book. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the.

Korteweg-de Vries and Nonlinear Schrodinger Equations: Qualitative Theory (Lecture Notes in Mathematics) Paperback – by Peter E. Zhidkov (Author) › Visit Amazon's Peter E. Zhidkov Page. Find all the books, read about the author, and more.

Author: Peter E. Zhidkov. Korteweg-de Vries and Nonlinear Schrödinger Equations: Qualitative Theory. Authors:.

graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are. This was originally noted by Zhidkov [Zhi01], in the context of Korteweg-de Vries (KdV) equation and cubic nonlinear Schrödinger (NLS) equation on T.

In the last years this approach has been. The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation.

The energy-critical nonlinear Schrödinger equation. So intense femtosecond pulse propagation in a silica fibre, strictly speaking, should not be calculated using the modified Korteweg-de Vries equation (I) and not even by the formula (I) specifying the linear dispersion of the medium, but by a more complex system Korteweg-de Vries and Nonlinear Schrödinger Equations book non-linear equations (), which takes into account also the.

The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics.

It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation.

Particularly useful tools in studying the nonlinear Schrodinger equation. This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation.

A concise and self-contained treatment of background. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation.

With Herbert Koch and Daniel Tătaru, Vișan is the author of the book Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps (Birkhäuser/Springer, ).

Her research papers include. The Korteweg–de Vries equation $u_t + uu_x + u_{xxx} = 0$ is a nonlinear partial differential equation arising in the study of a number of different physical systems, e.g., water waves, plasma physics, anharmonic lattices, and elastic rods.

Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps (Oberwolfach Seminars Book 45) - Kindle edition by Koch, Herbert, Tataru, Daniel, Vişan, Monica, Tataru, Daniel, Vişan, Monica.

springer, The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation.

The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing. Keyword: Korteweg-de Vries non-linear equation, exponential stability, time-delay, Lyapunov functional. 1 Introduction and main results InJohn Scott Russell observed for the rst time in a Scottish canal a solitary wave, also called soliton, which propagates without deformation in a nonlinear and dispersive medium.

Evolutionary equations. Results on existence -- The (generalized) Korteweg-de Vries equation (KdVE) -- The nonlinear Schrodinger equation (NLSE) -- On the blowing up of solutions -- Additional remarks -- Ch.

Stationary problems -- Existence of solutions. An ODE approach -- Existence of solutions. A variational. The Korteweg–de Vries (KdV) equation is an integrable system and a model to describe waves on shallow water surfaces, and analytic solutions are derived by Gardner, etZabusky presented generalized KdV equations and a special case is the famous modified KdV (mKdV) equation which possesses various of applications.

Historical Essay The Vries Format Equation A Korteweg-de. To be published, Abstract. Deconinck and Eve Browning Cole Body Mind And Gender Summary T. Korteweg and G. A wave can make a leaf bob up and down on the water, but it cannot move the leaf. (), vol. Korteweg–de Vries Equation [8] The KdV equation is a finite amplitude “fairly long” (i.e., weakly.

AbstractWe show the existence of positive bound and ground states for a system of coupled nonlinear Schrödinger–Korteweg–de Vries equations.

More precisely, we prove that there exists a positive radially symmetric ground state if either the coupling coefficient satisfies β > Λ {\beta>\Lambda} (for an appropriate constant Λ > 0 {\Lambda>0}) or if β > 0 {\beta>0} under appropriate.

The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or the Korteweg-de Vries equation.

Introduction Notation Chapter 1. Evolutionary equations. Results on existance The (generalized Korteweg-de Vries equation (KdVE) The nonlinear Schroedinger equation (NLSE) On the blowing up of solutions Additional remarks Chapter 2. Stationary problems Existence of solutions. An ODE approach Existence of solutions.

Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons.Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons.

45 references.Introduction Notation Chapter 1. Evolutionary equations. Results on existance The (generalized Korteweg-de Vries equation (KdVE) The nonlinear Schrödinger equation (NLSE) On the blowing up of solutions Additional remarks Chapter 2.

Stationary problems Existence of solutions. An ODE approach Existence of : \$