Solitons

An Introduction

Author: P. G. Drazin,R. S. Johnson

Publisher: Cambridge University Press

ISBN: 9780521336550

Category: Mathematics

Page: 226

View: 6088

This textbook is an introduction to the theory of solitons in the physical sciences.

Bäcklund and Darboux Transformations

Geometry and Modern Applications in Soliton Theory

Author: C. Rogers,W. K. Schief

Publisher: Cambridge University Press

ISBN: 9780521012881

Category: Mathematics

Page: 413

View: 3350

Explores deep and fascinating connections between a ubiquitous class of physically important waves known as solitons.

A Modern Introduction to the Mathematical Theory of Water Waves

Author: R. S. Johnson

Publisher: Cambridge University Press

ISBN: 9780521598323

Category: Mathematics

Page: 445

View: 8058

This text considers classical and modern problems in linear and non-linear water-wave theory.

Nonlinear Systems

Author: P. G. Drazin

Publisher: Cambridge University Press

ISBN: 9780521406680

Category: Mathematics

Page: 317

View: 5904

A coherent treatment of nonlinear systems covering chaos, fractals, and bifurcation, as well as equilibrium, stability, and nonlinear oscillations. The systems treated are mostly of difference and differential equations. The author introduces the mathematical properties of nonlinear systems as an integrated theory, rather than simply presenting isolated fashionable topics. The topics are discussed in as concrete a way as possible, worked examples and problems are used to motivate and illustrate the general principles. More advanced parts of the text are denoted by asterisks, thus making it ideally suited to both undergraduate and graduate courses.

Glimpses of Soliton Theory

The Algebra and Geometry of Nonlinear PDEs

Author: Alex Kasman

Publisher: American Mathematical Soc.

ISBN: 0821852450

Category: Mathematics

Page: 304

View: 7611

Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass -functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make this advanced subject accessible to any undergraduate math major, numerous worked examples and thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package Mathematica« to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a self-study, one-semester special topics, or "capstone" course.

Solitons

Differential Equations, Symmetries and Infinite Dimensional Algebras

Author: T. Miwa,M. Jimbo,E. Date

Publisher: Cambridge University Press

ISBN: 9780521561617

Category: Mathematics

Page: 108

View: 9620

The goal of this book is to investigate the high degree of symmetry that lies hidden in integrable systems.

Physics of Solitons

Author: Thierry Dauxois,Michel Peyrard

Publisher: Cambridge University Press

ISBN: 0521854210

Category: Mathematics

Page: 422

View: 478

This textbook gives an instructive view of solitons and their applications for advanced students of physics.

Wave Motion

Author: J. Billingham,A. C. King

Publisher: Cambridge University Press

ISBN: 1316583910

Category: Mathematics

Page: N.A

View: 5254

Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.

Nonlinear Waves, Solitons and Chaos

Author: Eryk Infeld,George Rowlands

Publisher: Cambridge University Press

ISBN: 9780521635578

Category: Mathematics

Page: 391

View: 2228

The second edition of a highly successful book on nonlinear waves, solitons and chaos.

Solitons, Instantons, and Twistors

Author: Maciej Dunajski

Publisher: Oxford University Press

ISBN: 0198570627

Category: Mathematics

Page: 359

View: 7351

The book provides a self-contained and accessible introduction to elementary twistor theory; a technique for solving differential equations in applied mathematics and theoretical physics. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basicdifferential geometry, complex manifold theory and the exterior differential system.

Scaling, Self-similarity, and Intermediate Asymptotics

Dimensional Analysis and Intermediate Asymptotics

Author: G. I. Barenblatt

Publisher: Cambridge University Press

ISBN: 9780521435222

Category: Mathematics

Page: 386

View: 1170

Scaling (power-type) laws reveal the fundamental property of the phenomena--self similarity. Self-similar (scaling) phenomena repeat themselves in time and/or space. The property of self-similarity simplifies substantially the mathematical modeling of phenomena and its analysis--experimental, analytical and computational. The book begins from a non-traditional exposition of dimensional analysis, physical similarity theory and general theory of scaling phenomena. Classical examples of scaling phenomena are presented. It is demonstrated that scaling comes on a stage when the influence of fine details of initial and/or boundary conditions disappeared but the system is still far from ultimate equilibrium state (intermediate asymptotics). It is explained why the dimensional analysis as a rule is insufficient for establishing self-similarity and constructing scaling variables. Important examples of scaling phenomena for which the dimensional analysis is insufficient (self-similarities of the second kind) are presented and discussed. A close connection of intermediate asymptotics and self-similarities of the second kind with a fundamental concept of theoretical physics, the renormalization group, is explained and discussed. Numerous examples from various fields--from theoretical biology to fracture mechanics, turbulence, flame propagation, flow in porous strata, atmospheric and oceanic phenomena are presented for which the ideas of scaling, intermediate asymptotics, self-similarity and renormalization group were of decisive value in modeling.

An Introduction to Stochastic Dynamics

Author: Jinqiao Duan

Publisher: Cambridge University Press

ISBN: 1107075394

Category: Mathematics

Page: 307

View: 1351

An accessible introduction for applied mathematicians to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty.

Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science

Author: Monica Cojocaru,Ilias S. Kotsireas,Roman Makarov,Roderick Melnik,Hasan Shodiev

Publisher: Springer

ISBN: 3319123076

Category: Computers

Page: 555

View: 6076

The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26—30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics and its areas of applications.

Solitons, Nonlinear Evolution Equations and Inverse Scattering

Author: Mark J. Ablowitz,P. A. Clarkson

Publisher: Cambridge University Press

ISBN: 9780521387309

Category: Mathematics

Page: 516

View: 7136

This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

Applied Wave Mathematics

Selected Topics in Solids, Fluids, and Mathematical Methods

Author: Ewald Quak,Tarmo Soomere

Publisher: Springer Science & Business Media

ISBN: 3642005853

Category: Mathematics

Page: 471

View: 4667

This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.

Applied Asymptotic Analysis

Author: Peter David Miller

Publisher: American Mathematical Soc.

ISBN: 0821840789

Category: Mathematics

Page: 467

View: 4157

"The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects."--BOOK JACKET.

Scaling

Author: G. I. Barenblatt

Publisher: Cambridge University Press

ISBN: 0521826578

Category: Mathematics

Page: 171

View: 3195

The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.

Introduction to Symmetry Analysis Paperback with CD-ROM

Author: Brian Cantwell

Publisher: Cambridge University Press

ISBN: 9780521777407

Category: Mathematics

Page: 612

View: 9207

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

Solitons, Instantons, and Twistors

Author: Maciej Dunajski

Publisher: Oxford University Press

ISBN: 0198570627

Category: Mathematics

Page: 359

View: 9576

The book provides a self-contained and accessible introduction to elementary twistor theory; a technique for solving differential equations in applied mathematics and theoretical physics. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basicdifferential geometry, complex manifold theory and the exterior differential system.