On The Theory Of Weak Turbulence For The Nonlinear Schrodinger Equation
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On The Theory Of Weak Turbulence For The Nonlinear Schr Dinger Equation
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Author : Miguel Escobedo
language : en
Publisher:
Release Date : 2015
On The Theory Of Weak Turbulence For The Nonlinear Schr Dinger Equation written by Miguel Escobedo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Nonlinear systems categories.
We study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. We define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. We also prove the existence of a family of solutions that exhibit pulsating behavior.
On The Theory Of Weak Turbulence For The Nonlinear Schrodinger Equation
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Author : M. Escobedo
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-27
On The Theory Of Weak Turbulence For The Nonlinear Schrodinger Equation written by M. Escobedo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-27 with Mathematics categories.
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
On A Kinetic Equation Arising In Weak Turbulence Theory For The Nonlinear Schr Dinger Equation
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Author : Arthur H. M. Kierkels
language : en
Publisher:
Release Date : 2016
On A Kinetic Equation Arising In Weak Turbulence Theory For The Nonlinear Schr Dinger Equation written by Arthur H. M. Kierkels and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Nonlinear Waves And Weak Turbulence
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Author : FITZMAURICE
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Waves And Weak Turbulence written by FITZMAURICE and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This book is an outgrowth of the NSF-CBMS conference Nonlinear Waves £3 Weak Turbulence held at Case Western Reserve University in May 1992. The principal speaker at the conference was Professor V. E. Zakharov who delivered a series of ten lectures outlining the historical and ongoing developments in the field. Some twenty other researchers also made presentations and it is their work which makes up the bulk of this text. Professor Zakharov's opening chapter serves as a general introduction to the other papers, which for the most part are concerned with the application of the theory in various fields. While the word "turbulence" is most often associated with f:l. uid dynamics it is in fact a dominant feature of most systems having a large or infinite number of degrees of freedom. For our purposes we might define turbulence as the chaotic behavior of systems having a large number of degrees of freedom and which are far from thermodynamic equilibrium. Work in field can be broadly divided into two areas: • The theory of the transition from smooth laminar motions to the disordered motions characteristic of turbulence. • Statistical studies of fully developed turbulent systems. In hydrodynamics, work on the transition question dates back to the end of the last century with pioneering contributions by Osborne Reynolds and Lord Rayleigh.
The Nonlinear Schr Dinger Equation
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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30
The Nonlinear Schr Dinger Equation written by Catherine Sulem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-30 with Mathematics categories.
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
Extended Abstracts 2021 2022
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Author : Duván Cardona
language : en
Publisher: Springer Nature
Release Date : 2024-02-28
Extended Abstracts 2021 2022 written by Duván Cardona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-28 with Mathematics categories.
This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics: 1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown. 2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.
Statistical Physics Of Non Equilibrium Quantum Phenomena
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Author : Yves Pomeau
language : en
Publisher: Springer Nature
Release Date : 2019-11-29
Statistical Physics Of Non Equilibrium Quantum Phenomena written by Yves Pomeau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-29 with Science categories.
This book provides an introduction to topics in non-equilibrium quantum statistical physics for both mathematicians and theoretical physicists. The first part introduces a kinetic equation, of Kolmogorov type, which is needed to describe an isolated atom (actually, in experiments, an ion) under the effect of a classical pumping electromagnetic field which keeps the atom in its excited state(s) together with the random emission of fluorescence photons which put it back into its ground state. The quantum kinetic theory developed in the second part is an extension of Boltzmann's classical (non-quantum) kinetic theory of a dilute gas of quantum bosons. This is the source of many interesting fundamental questions, particularly because, if the temperature is low enough, such a gas is known to have at equilibrium a transition, the Bose–Einstein transition, where a finite portion of the particles stay in the quantum ground state. An important question considered is how a Bose gas condensate develops in time if its energy is initially low enough.
Classical Kinetic Theory Of Weakly Turbulent Nonlinear Plasma Processes
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Author : Peter H. Yoon
language : en
Publisher: Cambridge University Press
Release Date : 2019-09-12
Classical Kinetic Theory Of Weakly Turbulent Nonlinear Plasma Processes written by Peter H. Yoon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Science categories.
A systematic overview of the kinetic theory of weak plasma turbulence, including the foundational concepts and mathematical and technical details.
Nonlinear Pde S In Condensed Matter And Reactive Flows
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Author : Henri Berestycki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Pde S In Condensed Matter And Reactive Flows written by Henri Berestycki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Nonlinear partial differential equations abound in modern physics. The problems arising in these fields lead to fascinating questions and, at the same time, progress in understanding the mathematical structures is of great importance to the models. Nevertheless, activity in one of the approaches is not always sufficiently in touch with developments in the other field. The book presents the joint efforts of mathematicians and physicists involved in modelling reactive flows, in particular superconductivity and superfluidity. Certain contributions are fundamental to an understanding of such cutting-edge research topics as rotating Bose-Einstein condensates, Kolmogorov-Zakharov solutions for weak turbulence equations, and the propagation of fronts in heterogeneous media.
Introduction To The Theory Of Incoherent Scattering Of Radar Waves From Plasmas
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Author : Hans László Pécseli
language : en
Publisher: Springer Nature
Release Date : 2025-03-26
Introduction To The Theory Of Incoherent Scattering Of Radar Waves From Plasmas written by Hans László Pécseli and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-26 with Science categories.
This book introduces the theory behind the incoherent scattering of electromagnetic waves (radar waves) by free electrons—a key technique for studying critical parameters of the Earth’s ionosphere. Starting with scattering by statistically independent electrons, including magnetized cases, the book progressively develops a comprehensive model. This framework is extended to include ‘dressed particles’, accounting for long-range Coulomb interactions between charged particles. A consistent approach to incorporating particle collisions is presented, with an example of charge exchange interactions for illustration. Appendices provide essential background material, ensuring the content is accessible to readers. Based on lectures delivered at the University of Tromsø, Norway, this book is designed for Masters and PhD students. It assumes a basic understanding of electromagnetism and plasma physics, including plasma waves and electrostatic phenomena. Familiarity with kinetic plasma theory and the collisionless Vlasov equation is beneficial but not mandatory.