Solitary Waves In Nonlinear Dirac Equation
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Author | : Nabile Boussaïd |
Publisher | : American Mathematical Soc. |
Total Pages | : 297 |
Release | : 2019-11-21 |
Genre | : Education |
ISBN | : 1470443953 |
Download Nonlinear Dirac Equation: Spectral Stability of Solitary Waves Book in PDF, Epub and Kindle
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. 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 general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.
Author | : Nabile Boussaïd |
Publisher | : |
Total Pages | : 297 |
Release | : 1920 |
Genre | : Differential equations, Partial |
ISBN | : 9781470454227 |
Download Nonlinear Dirac Equation Book in PDF, Epub and Kindle
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. 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 general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2015 |
Genre | : |
ISBN | : |
Download Solitary Waves in Nonlinear Dirac Equation Book in PDF, Epub and Kindle
This report describes the implementation of nonlinear Dirac equations in the calculation of solitary waves. Conclusions and comments on quantum elasticity are also included.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Download Solitary Waves in the Nonlinear Dirac Equation in the Presence of External Driving Forces Book in PDF, Epub and Kindle
Author | : R. Grimshaw |
Publisher | : WIT Press |
Total Pages | : 209 |
Release | : 2007 |
Genre | : Science |
ISBN | : 1845641574 |
Download Solitary Waves in Fluids Book in PDF, Epub and Kindle
Edited by R.H.J. Grimshaw, this book covers the topic of solitary waves in fluids.
Author | : Victoriano Carmona |
Publisher | : Springer |
Total Pages | : 428 |
Release | : 2018-09-15 |
Genre | : Science |
ISBN | : 3319667661 |
Download Nonlinear Systems, Vol. 1 Book in PDF, Epub and Kindle
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.
Author | : Claire David |
Publisher | : Bentham Science Publishers |
Total Pages | : 267 |
Release | : 2010 |
Genre | : Science |
ISBN | : 1608051404 |
Download Solitary Waves in Fluid Media Book in PDF, Epub and Kindle
Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations which govern solitary waves, from the Korteweg-de Vries equation to the nonlinear Schrodinger equation, in the 1960's. From that moment, a huge amount of theoretical works can be found on solitary waves. Due to the fact that many physical phenomena can be described by a soliton model, applications have followed each other, in telecommunications
Author | : Victor Christianto |
Publisher | : Infinite Study |
Total Pages | : 5 |
Release | : 2023-01-01 |
Genre | : Science |
ISBN | : |
Download Towards Soliton Computer Based on Solitary Wave Solution of Maxwell Dirac equation: A Plausible Alternative to Manakov System Book in PDF, Epub and Kindle
In recent years, there are a number of proposals to consider collision-based soliton computer based on certain chemical reactions, namely Belousov-Zhabotinsky reaction, which leads to soliton solutions of coupled Nonlinear Schroedinger equations. They are called Manakov System. But it seems to us that such a soliton computer model can also be based on solitary wave solution of Maxwell-Dirac equation, which reduces to Choquard equation. And soliton solution of Choquard equation has been investigated by many researchers, therefore it seems more profound from physics perspective. However, we consider both schemes of soliton computer are equally possible. More researches are needed to verify our proposition.
Author | : Anatoly M Kamchatnov |
Publisher | : World Scientific |
Total Pages | : 399 |
Release | : 2000-09-05 |
Genre | : Science |
ISBN | : 9814492434 |
Download Nonlinear Periodic Waves And Their Modulations: An Introductory Course Book in PDF, Epub and Kindle
Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to treat various problems in nonlinear wave theory. Therefore it is topical to describe recent developments of the Whitham theory in a clear and simple form suitable for applications in various branches of physics.This book develops the techniques of the theory of nonlinear periodic waves at elementary level and in great pedagogical detail. It provides an introduction to a Whitham's theory of modulation in a form suitable for applications. The exposition is based on a thorough analysis of representative examples taken from fluid mechanics, nonlinear optics and plasma physics rather than on the formulation and study of a mathematical theory. Much attention is paid to physical motivations of the mathematical methods developed in the book. The main applications considered include the theory of collisionless shock waves in dispersive systems and the nonlinear theory of soliton formation in modulationally unstable systems. Exercises are provided to amplify the discussion of important topics such as singular perturbation theory, Riemann invariants, the finite gap integration method, and Whitham equations and their solutions.
Author | : M. Toda |
Publisher | : Springer Science & Business Media |
Total Pages | : 396 |
Release | : 1989-11-30 |
Genre | : Mathematics |
ISBN | : 9780792304425 |
Download Nonlinear Waves and Solitons Book in PDF, Epub and Kindle
' it is certainly a beautiful presentation, very well adapted to teaching beginners. I am sure this book will be successful.' Inverse Problems, 1990