Nonlinear Dispersive Partial Differential Equations and Inverse Scattering

Download Nonlinear Dispersive Partial Differential Equations and Inverse Scattering PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 1493998064
Total Pages : 528 pages
Book Rating : 4.4/5 (939 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dispersive Partial Differential Equations and Inverse Scattering by : Peter D. Miller

Download or read book Nonlinear Dispersive Partial Differential Equations and Inverse Scattering written by Peter D. Miller and published by Springer Nature. This book was released on 2019-11-14 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download Nonlinear Dispersive Equations PDF Online Free

Author :
Publisher : Springer Nature
ISBN 13 : 3030914275
Total Pages : 596 pages
Book Rating : 4.0/5 (39 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dispersive Equations by : Christian Klein

Download or read book Nonlinear Dispersive Equations written by Christian Klein and published by Springer Nature. This book was released on 2021 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Nonlinear Dispersive Equations

Download Introduction to Nonlinear Dispersive Equations PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 1493921819
Total Pages : 308 pages
Book Rating : 4.4/5 (939 download)

DOWNLOAD NOW!


Book Synopsis Introduction to Nonlinear Dispersive Equations by : Felipe Linares

Download or read book Introduction to Nonlinear Dispersive Equations written by Felipe Linares and published by Springer. This book was released on 2014-12-15 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introduction to Nonlinear Dispersive Equations builds upon the success of the first edition by the addition of updated material on the main topics, an expanded bibliography, and new exercises. Assuming only basic knowledge of complex analysis and integration theory, this book will enable graduate students and researchers to enter this actively developing field.

Dispersive Partial Differential Equations

Download Dispersive Partial Differential Equations PDF Online Free

Author :
Publisher : Cambridge University Press
ISBN 13 : 1316694585
Total Pages : 203 pages
Book Rating : 4.3/5 (166 download)

DOWNLOAD NOW!


Book Synopsis Dispersive Partial Differential Equations by : M. Burak Erdoğan

Download or read book Dispersive Partial Differential Equations written by M. Burak Erdoğan and published by Cambridge University Press. This book was released on 2016-05-03 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing field which has become exceedingly technical in recent years. With this book, the authors provide a self-contained and accessible introduction for graduate or advanced undergraduate students in mathematics, engineering, and the physical sciences. Both classical and modern methods used in the field are described in detail, concentrating on the model cases that simplify the presentation without compromising the deep technical aspects of the theory, thus allowing students to learn the material in a short period of time. This book is appropriate both for self-study by students with a background in analysis, and for teaching a semester-long introductory graduate course in nonlinear dispersive PDEs. Copious exercises are included, and applications of the theory are also presented to connect dispersive PDEs with the more general areas of dynamical systems and mathematical physics.

Solitons and the Inverse Scattering Transform

Download Solitons and the Inverse Scattering Transform PDF Online Free

Author :
Publisher : SIAM
ISBN 13 : 089871477X
Total Pages : 433 pages
Book Rating : 4.8/5 (987 download)

DOWNLOAD NOW!


Book Synopsis Solitons and the Inverse Scattering Transform by : Mark J. Ablowitz

Download or read book Solitons and the Inverse Scattering Transform written by Mark J. Ablowitz and published by SIAM. This book was released on 2006-05-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation.

Nonlinear Dispersive Wave Systems

Download Nonlinear Dispersive Wave Systems PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9814554960
Total Pages : 683 pages
Book Rating : 4.8/5 (145 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dispersive Wave Systems by : Lokenath Debnath

Download or read book Nonlinear Dispersive Wave Systems written by Lokenath Debnath and published by World Scientific. This book was released on 1992-09-09 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a comprehensive account of major developments in the theory and applications of nonlinear dispersive waves, nonlinear water waves, KdV and nonlinear Schrodinger equations, Davey-Stewartson equation, Benjamin-Ono equation and nonlinear instability phenomena. In order to give the book a wider readership, chapters have been written by internationally known researchers who have made significant contributions to nonlinear waves and nonlinear instability. This volume will be invaluable to applied mathematicians, physicists, geophysicists, oceanographers, engineering scientists, and to anyone interested in nonlinear dynamics.

Nonlinear Dispersive Equations

Download Nonlinear Dispersive Equations PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821841432
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dispersive Equations by : Terence Tao

Download or read book Nonlinear Dispersive Equations written by Terence Tao and published by American Mathematical Soc.. This book was released on 2006 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems.".

Nonlinear Partial Differential Equations for Scientists and Engineers

Download Nonlinear Partial Differential Equations for Scientists and Engineers PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1489928464
Total Pages : 602 pages
Book Rating : 4.4/5 (899 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Partial Differential Equations for Scientists and Engineers by : Lokenath Debnath

Download or read book Nonlinear Partial Differential Equations for Scientists and Engineers written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.

Dispersive Equations and Nonlinear Waves

Download Dispersive Equations and Nonlinear Waves PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 3034807368
Total Pages : 310 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!


Book Synopsis Dispersive Equations and Nonlinear Waves by : Herbert Koch

Download or read book Dispersive Equations and Nonlinear Waves written by Herbert Koch and published by Springer. This book was released on 2014-07-14 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.​

Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations

Download Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1000708683
Total Pages : 388 pages
Book Rating : 4.0/5 (7 download)

DOWNLOAD NOW!


Book Synopsis Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations by : Pham Loi Vu

Download or read book Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations written by Pham Loi Vu and published by CRC Press. This book was released on 2019-11-11 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations is devoted to inverse scattering problems (ISPs) for differential equations and their application to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, partial differential equations, equations of mathematical physics, and functions of a complex variable. This book is intended for a wide community working with inverse scattering problems and their applications; in particular, there is a traditional community in mathematical physics. In this monograph, the problems are solved step-by-step, and detailed proofs are given for the problems to make the topics more accessible for students who are approaching them for the first time. Features • The unique solvability of ISPs are proved. The scattering data of the considered inverse scattering problems (ISPs) are described completely. • Solving the associated initial value problem or initial-boundary value problem for the nonlinear evolution equations (NLEEs) is carried out step-by-step. Namely, the NLEE can be written as the compatibility condition of two linear equations. The unknown boundary values are calculated with the help of the Lax (generalized) equation, and then the time-dependent scattering data (SD) are constructed from the initial and boundary conditions. • The potentials are recovered uniquely in terms of time-dependent SD, and the solution of the NLEEs is expressed uniquely in terms of the found solutions of the ISP. • Since the considered ISPs are solved well, then the SPs generated by two linear equations constitute the inverse scattering method (ISM). The application of the ISM to solving the NLEEs is consistent and is effectively embedded in the schema of the ISM.

The Legacy of the Inverse Scattering Transform in Applied Mathematics

Download The Legacy of the Inverse Scattering Transform in Applied Mathematics PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821831615
Total Pages : 346 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!


Book Synopsis The Legacy of the Inverse Scattering Transform in Applied Mathematics by : J. L. Bona

Download or read book The Legacy of the Inverse Scattering Transform in Applied Mathematics written by J. L. Bona and published by American Mathematical Soc.. This book was released on 2002 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Swift progress and new applications characterize the area of solitons and the inverse scattering transform. There are rapid developments in current nonlinear optical technology: Larger intensities are more available; pulse widths are smaller; relaxation times and damping rates are less significant. In keeping with these advancements, exactly integrable soliton equations, such as $3$-wave resonant interactions and second harmonic generation, are becoming more and more relevant inexperimental applications. Techniques are now being developed for using these interactions to frequency convert high intensity sources into frequency regimes where there are no lasers. Other experiments involve using these interactions to develop intense variable frequency sources, opening up even morepossibilities. This volume contains new developments and state-of-the-art research arising from the conference on the ``Legacy of the Inverse Scattering Transform'' held at Mount Holyoke College (South Hadley, MA). Unique to this volume is the opening section, ``Reviews''. This part of the book provides reviews of major research results in the inverse scattering transform (IST), on the application of IST to classical problems in differential geometry, on algebraic and analytic aspects ofsoliton-type equations, on a new method for studying boundary value problems for integrable partial differential equations (PDEs) in two dimensions, on chaos in PDEs, on advances in multi-soliton complexes, and on a unified approach to integrable systems via Painleve analysis. This conference provided aforum for general exposition and discussion of recent developments in nonlinear waves and related areas with potential applications to other fields. The book will be of interest to graduate students and researchers interested in mathematics, physics, and engineering.

Inverse Scattering Transform and Solitons for Matrix Nonlinear Schrodinger Systems and for the Defocusing Ablowitz-Ladik Equation with Nonzero Boundary Conditions

Download Inverse Scattering Transform and Solitons for Matrix Nonlinear Schrodinger Systems and for the Defocusing Ablowitz-Ladik Equation with Nonzero Boundary Conditions PDF Online Free

Author :
Publisher :
ISBN 13 :
Total Pages : 159 pages
Book Rating : 4.:/5 (112 download)

DOWNLOAD NOW!


Book Synopsis Inverse Scattering Transform and Solitons for Matrix Nonlinear Schrodinger Systems and for the Defocusing Ablowitz-Ladik Equation with Nonzero Boundary Conditions by : Alyssa Kayelin Ortiz

Download or read book Inverse Scattering Transform and Solitons for Matrix Nonlinear Schrodinger Systems and for the Defocusing Ablowitz-Ladik Equation with Nonzero Boundary Conditions written by Alyssa Kayelin Ortiz and published by . This book was released on 2019 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scalar nonlinear Schrodinger (NLS) equation is a nonlinear partial differential equation that models many of the world’s weakly nonlinear dispersive wave phenomena. This dissertation discusses two important variants of NLS: (i) the matrix NLS (MNLS), applicable in low-temperature physics and nonlinear optics, and (ii) the defocusing Ablowitz-Ladik equation, a variant of scalar NLS, continuous in time but discrete in space. In Chapter 2, the Inverse Scattering Transform (IST) is used to investigate four distinct MNLS systems, proposed by Tsuchida, shown to be integrable and to have solitary wave solutions (i.e. solitons). Two of these systems correspond to focusing and defocusing MNLS equations; the other two exhibit mixed-sign Minkowski-type nonlinear terms. In this chapter, the IST is developed with zero boundary conditions (ZBC) for all four systems, completely characterizing the solution’s spectrum. Novel soliton solutions are also derived for the mixed-sign MNLS systems. In Chapter 3, these MNLS systems are analyzed with nonzero boundary conditions (NZBC) using IST. The NZBC introduce challenges due to the existence of branch points in the spectral parameter, but the reward is a richer set of soliton solutions, such as dark solitons, periodic solutions, and rational solutions (i.e., rogue waves). In Chapter 4, the IST is developed for the defocusing Ablowitz-Ladik (AL) equation with an arbitrarily large nonzero background. It is well known that continuous and discrete focusing NLS systems exhibit modulational instability, i.e., the instability of a constant background with respect to long wavelength perturbations. In the continuous scalar defocusing NLS, modulational instability is never observed, regardless of background size. However, Ohta and Yang recently showed that the defocusing AL equation with a background greater than one becomes modulationally unstable, admitting rational solutions that are the analog of those found in its focusing counterpart. These recent findings motivate our investigation since the IST for the defocusing AL equation with NZBC has only previously been developed under the assumption of a small background less than one. The results presented in Chapter 2 were published in Studies in Applied Mathematics, and those in Chapters 3 and 4 have been submitted for publication.

Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1

Download Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821811252
Total Pages : 494 pages
Book Rating : 4.8/5 (112 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 by : Basil Nicolaenko

Download or read book Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1986 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations, this title contains papers grouped in sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems.

Nonlinear Partial Differential Equations

Download Nonlinear Partial Differential Equations PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 3034801912
Total Pages : 156 pages
Book Rating : 4.0/5 (348 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Partial Differential Equations by : Luis A. Caffarelli

Download or read book Nonlinear Partial Differential Equations written by Luis A. Caffarelli and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.

Nonlinear Systems of Partial Differential Equations in Applied Mathematics

Download Nonlinear Systems of Partial Differential Equations in Applied Mathematics PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896891
Total Pages : 490 pages
Book Rating : 4.8/5 (968 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Systems of Partial Differential Equations in Applied Mathematics by : Basil Nicolaenko

Download or read book Nonlinear Systems of Partial Differential Equations in Applied Mathematics written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes of 47 papers focus on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations. The papers both survey recent results and indicate future research trends in these vital and rapidly developing branches of PDEs. The editor has grouped the papers loosely into the following five sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems. However, the variety of the subjects discussed as well as their many interwoven trends demonstrate that it is through interactive advances that such rapid progress has occurred. These papers require a good background in partial differential equations. Many of the contributors are mathematical physicists, and the papers are addressed to mathematical physicists (particularly in perturbed integrable systems), as well as to PDE specialists and applied mathematicians in general.

Nonlinear Dispersive Equations

Download Nonlinear Dispersive Equations PDF Online Free

Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821848976
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)

DOWNLOAD NOW!


Book Synopsis Nonlinear Dispersive Equations by : Jaime Angulo Pava

Download or read book Nonlinear Dispersive Equations written by Jaime Angulo Pava and published by American Mathematical Soc.. This book was released on 2009 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Solitons

Download Solitons PDF Online Free

Author :
Publisher : CUP Archive
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4./5 ( download)

DOWNLOAD NOW!


Book Synopsis Solitons by : P. G. Drazin

Download or read book Solitons written by P. G. Drazin and published by CUP Archive. This book was released on 1986 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: