Nonlinear Dispersive Partial Differential Equations And Inverse Scattering
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Nonlinear Dispersive Partial Differential Equations And Inverse Scattering
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Author : Peter D. Miller
language : en
Publisher: Springer Nature
Release Date : 2019-11-14
Nonlinear Dispersive Partial Differential Equations And Inverse Scattering written by Peter D. Miller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
This volume contains lectures and invited papers from the Focus Program on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" held at the Fields Institute from July 31-August 18, 2017. The conference brought together researchers in completely integrable systems and PDE with the goal of advancing the understanding of qualitative and long-time behavior in dispersive nonlinear equations. The program included Percy Deift’s Coxeter lectures, which appear in this volume together with tutorial lectures given during the first week of the focus program. The research papers collected here include new results on the focusing nonlinear Schrödinger (NLS) equation, the massive Thirring model, and the Benjamin-Bona-Mahoney equation as dispersive PDE in one space dimension, as well as the Kadomtsev-Petviashvili II equation, the Zakharov-Kuznetsov equation, and the Gross-Pitaevskii equation as dispersive PDE in two space dimensions. The Focus Program coincided with the fiftieth anniversary of the discovery by Gardner, Greene, Kruskal and Miura that the Korteweg-de Vries (KdV) equation could be integrated by exploiting a remarkable connection between KdV and the spectral theory of Schrodinger's equation in one space dimension. This led to the discovery of a number of completely integrable models of dispersive wave propagation, including the cubic NLS equation, and the derivative NLS equation in one space dimension and the Davey-Stewartson, Kadomtsev-Petviashvili and Novikov-Veselov equations in two space dimensions. These models have been extensively studied and, in some cases, the inverse scattering theory has been put on rigorous footing. It has been used as a powerful analytical tool to study global well-posedness and elucidate asymptotic behavior of the solutions, including dispersion, soliton resolution, and semiclassical limits.
Nonlinear Dispersive Equations
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Author : Christian Klein
language : en
Publisher:
Release Date : 2021
Nonlinear Dispersive Equations written by Christian Klein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose-Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin-Ono, Davey-Stewartson, and Kadomtsev-Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Nonlinear Dispersive Equations
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Author : Christian Klein
language : en
Publisher: Springer Nature
Release Date : 2022-02-23
Nonlinear Dispersive Equations written by Christian Klein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-23 with Mathematics categories.
Nonlinear Dispersive Equations are partial differential equations that naturally arise in physical settings where dispersion dominates dissipation, notably hydrodynamics, nonlinear optics, plasma physics and Bose–Einstein condensates. The topic has traditionally been approached in different ways, from the perspective of modeling of physical phenomena, to that of the theory of partial differential equations, or as part of the theory of integrable systems. This monograph offers a thorough introduction to the topic, uniting the modeling, PDE and integrable systems approaches for the first time in book form. The presentation focuses on three "universal" families of physically relevant equations endowed with a completely integrable member: the Benjamin–Ono, Davey–Stewartson, and Kadomtsev–Petviashvili equations. These asymptotic models are rigorously derived and qualitative properties such as soliton resolution are studied in detail in both integrable and non-integrable models. Numerical simulations are presented throughout to illustrate interesting phenomena. By presenting and comparing results from different fields, the book aims to stimulate scientific interactions and attract new students and researchers to the topic. To facilitate this, the chapters can be read largely independently of each other and the prerequisites have been limited to introductory courses in PDE theory.
Dispersive Partial Differential Equations
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Author : M. Burak Erdoğan
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-12
Dispersive Partial Differential Equations written by M. Burak Erdoğan 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 2016-05-12 with Mathematics categories.
Introduces nonlinear dispersive partial differential equations in a detailed yet elementary way without compromising the depth and richness of the subject.
Dispersive Equations And Nonlinear Waves
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Author : Herbert Koch
language : en
Publisher: Birkhäuser
Release Date : 2014-07-31
Dispersive Equations And Nonlinear Waves written by Herbert Koch and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 with Mathematics categories.
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 problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.
Nonlinear Dispersive Equations
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Author : Jaime Angulo Pava
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Nonlinear Dispersive Equations written by Jaime Angulo Pava 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 2009 with Mathematics categories.
This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied include Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.
Nonlinear Partial Differential Equations For Scientists And Engineers
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Author : Lokenath Debnath
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Nonlinear Partial Differential Equations For Scientists And Engineers written by Lokenath Debnath 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 2013-11-11 with Mathematics categories.
"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." - Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership.
Hamiltonian Partial Differential Equations And Applications
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Author : Philippe Guyenne
language : en
Publisher: Springer
Release Date : 2015-09-11
Hamiltonian Partial Differential Equations And Applications written by Philippe Guyenne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-11 with Mathematics categories.
This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.
Selected Papers On Analysis And Differential Equations
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Author : American Mathematical Society
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Selected Papers On Analysis And Differential Equations written by American Mathematical Society 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 2010 with Mathematics categories.
"Volume includes English translation of ten expository articles published in the Japanese journal Sugaku."
Functional Analytic Methods For Partial Differential Equations
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Author : Hiroshi Fujita
language : en
Publisher: Springer
Release Date : 2006-11-14
Functional Analytic Methods For Partial Differential Equations written by Hiroshi Fujita and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Proceedings of the International Conference on Functional Analysis and Its Application in Honor of Professor Tosio Kato, July 3-6, 1989, University of Tokyo, and the Symposium on Spectral and Scattering Theory, held July 7, 1989, at Gakushin University, Tokyo.