Singular Limits Of Dispersive Waves

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Singular Limits Of Dispersive Waves

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Author : N.M. Ercolani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Singular Limits Of Dispersive Waves written by N.M. Ercolani 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 Science categories.

Proceedings of a NATO ARW and of a Chaos, Order, and Patterns Panel sponsored workshop held in Lyons, France, July 8-12, 1991

Wigner Measure And Semiclassical Limits Of Nonlinear Schr Dinger Equations

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Author : Ping Zhang
language : en
Publisher: American Mathematical Soc.
Release Date :

Wigner Measure And Semiclassical Limits Of Nonlinear Schr Dinger Equations written by Ping Zhang 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 with Mathematics categories.

"This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrodinger equations," which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrodinger-type equations." "At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic."--BOOK JACKET.

Nonlinear Evolution Equations And Dynamical Systems Needs 94

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Author : Vladimir G Makhankov
language : en
Publisher: World Scientific
Release Date : 1995-04-26

Nonlinear Evolution Equations And Dynamical Systems Needs 94 written by Vladimir G Makhankov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-04-26 with categories.

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Important Developments In Soliton Theory

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Author : A.S. Fokas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Important Developments In Soliton Theory written by A.S. Fokas 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 Science categories.

In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.

Nonlinear Periodic Waves And Their Modulations

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Author : Anatoli? Mikha?lovich Kamchatnov
language : en
Publisher: World Scientific
Release Date : 2000

Nonlinear Periodic Waves And Their Modulations written by Anatoli? Mikha?lovich Kamchatnov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Science categories.

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.

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.

Differential Operators And Spectral Theory

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Author : M. Sh Birman
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Differential Operators And Spectral Theory written by M. Sh Birman 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 1999 with Mathematics categories.

This volume contains a collection of original papers in mathematical physics, spectral theory, and differential equations. The papers are dedicated to the outstanding mathematician, Professor M. Sh. Birman, on the occasion of his 70th birthday. Contributing authors are leading specialists and close professional colleagues of Birman. The main topics discussed are spectral and scattering theory of differential operators, trace formulas, and boundary value problems for PDEs. Several papers are devoted to the magnetic Schrodinger operator, which is within Birman's current scope of interests and recently has been studied extensively. Included is a detailed survey of his mathematical work and an updated list of his publications.This book is aimed at graduate students and specialists in the above-mentioned branches of mathematics and theoretical physicists. The biographical section will be of interest to readers concerned with the scientific activities of Birman and the history of those branches of analysis and spectral theory where his contributions were important and often decisive. Features: The first detailed survey of Birman's mathematical work; includes an updated bibliography. New material on the history of some branches of analysis. Prominent authors: Lieb, Agmon, Deift, Simon, Ladyzhenskaya, and others. All original works, containing new results in fields of great current interest.

Nonlinear Dispersive Waves

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Author : David Henry
language : en
Publisher: Springer Nature
Release Date : 2024-08-06

Nonlinear Dispersive Waves written by David Henry and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-06 with Mathematics categories.

This volume explores a number of exciting developments in the field of nonlinear dispersive waves with a particular focus on waves arising in the ocean. Chapters are based on talks given at the workshop “Nonlinear Dispersive Waves” that was held at University College Cork, Ireland, on April 24-25, 2023. Specific topics covered include: The recovery of steady rotational wave surface profiles; Hamiltonian models for the propagation of long gravity waves; Waves propagating at the surface of a fluid covered by floating ice plates; The use of spherical coordinates to describe arctic ocean waves; Boundary value problems related to the Muskat Problem. Nonlinear Dispersive Waves will appeal to researchers as well as graduate students interested in this active area of research.

Bilinear Integrable Systems From Classical To Quantum Continuous To Discrete

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Author : Ludwig Faddeev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-16

Bilinear Integrable Systems From Classical To Quantum Continuous To Discrete written by Ludwig Faddeev 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 2007-05-16 with Science categories.

On April 29, 1814 Napoleon landed on the island of Elba, surrounded with a personal army of 1200 men. The allies, Russia, Prussia, England and Austria, hadforcedhimintoexileafteranumberofverycostlydefeats;hewasdeprived ofallhistitles, butcouldkeepthetitleof"EmperorofElba". Historytellsusthat each morning he took long walks in the sun, reviewed his army each midday anddiscussedworldmatterswithnewlyappointedadvisors, followingthesame pattern everyday, to the great surprise of Campbell, the British of?cer who was to keep an eye on him. All this made everyone believe he was settled there for good. Napoleononcesaid:Elbaisbeautiful, butabitsmall. Elbawasde?nitely a source of inspiration; indeed, the early morning, March 6, 1815, Metternich, the chancellor of Austria was woken up by one of his aides with the stunning news that Napoleon had left Elba with his 1200 men and was marching to Paris with little resistance; A few days later he took up his throne again in the Tuileries. In spite of his insatiable hunger for battles and expansion, he is remembered as an important statesman. He was a pioneer in setting up much of the legal, administrative and political machinery in large parts of continental Europe. We gathered here in a lovely and quaint?shing port, Marciana Marina on theislandofElba, tocelebrateoneofthepioneersofintegrablesystems, Hirota Sensei, andthisattheoccasionofhisseventiethbirthday. Trainedasaphysicist in his home university Kyushu University, Professor Hirota earned his PhD in '61 at Northwestern University with Professor Siegert in the?eld of "Quantum Statistical mechanics". He wrote a widely appreciated Doctoral dissertation on "FunctionalIntegralrepresentationofthegrandpartitionfunction."