Partial Differential Equations And Solitary Waves Theory

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 53,8 Mb
Release : 2010-05-28
Category : Mathematics
ISBN : 9783642002519

Get Book

Partial Differential Equations and Solitary Waves Theory by Abdul-Majid Wazwaz Pdf

"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

Author : A. M. Wazwaz
Publisher : Unknown
Page : 758 pages
File Size : 47,6 Mb
Release : 2009
Category : Electronic
ISBN : OCLC:935271430

Get Book

Partial Differential Equations and Solitary Waves Theory by A. M. Wazwaz Pdf

Features methods for solving Partial Differential Equations (PDEs). This book covers solitary waves theory. It also handles nonlinear evolution equations by methods such as Hirota's bilinear method or the tanh-coth method.

Author : J. R. Bogning
Publisher : Dorrance Publishing
Page : 233 pages
File Size : 55,6 Mb
Release : 2019-12-13
Category : Science
ISBN : 9781644262801

Get Book

Mathematics for Nonlinear Physics by J. R. Bogning Pdf

Mathematics for Nonlinear Physics: Solitary Wave in the Center of the Resolution of Dispersive Nonlinear Partial Differential Equations By: J.R. Bogning Mathematics for Nonlinear Physics: Solitary Wave in the Center of the Resolution of Dispersive Nonlinear Partial Differential Equations is the result of ten years of high-level research on the dynamics of solitary waves. In the context of his different work in nonlinear physics, J.R. Bogning encountered differential equations with nonlinear partial derivatives whose search for solutions was not always obvious. But beyond the fact that these equations encountered were not always easy to integrate, the observation he made was that very few works proposed forced solitary wave solutions. So this book develops in detail new mathematical techniques to solve some types of nonlinear equations encountered in nonlinear physics. This book is unique in terms of its content; the theories developed inside are not in any other book. This book is the pioneer in the theory developed within it and will be the reference book from which other researchers and scientists will rely to extend and develop the mathematical concepts found there. Mastery of the properties and functions developed in the book will help to digitize solitary waves.

Author : Roger Knobel
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 44,9 Mb
Release : 2000
Category : Wave-motion, Theory of
ISBN : 9780821820391

Get Book

An Introduction to the Mathematical Theory of Waves by Roger Knobel Pdf

This book is based on an undergraduate course taught at the IAS/Park City Mathematics Institute (Utah) on linear and nonlinear waves. The first part of the text overviews the concept of a wave, describes one-dimensional waves using functions of two variables, provides an introduction to partial differential equations, and discusses computer-aided visualization techniques. The second part of the book discusses traveling waves, leading to a description of solitary waves and soliton solutions of the Klein-Gordon and Korteweg-deVries equations. The wave equation is derived to model the small vibrations of a taut string, and solutions are constructed via d'Alembert's formula and Fourier series.The last part of the book discusses waves arising from conservation laws. After deriving and discussing the scalar conservation law, its solution is described using the method of characteristics, leading to the formation of shock and rarefaction waves. Applications of these concepts are then given for models of traffic flow. The intent of this book is to create a text suitable for independent study by undergraduate students in mathematics, engineering, and science. The content of the book is meant to be self-contained, requiring no special reference material. Access to computer software such as MathematicaR, MATLABR, or MapleR is recommended, but not necessary. Scripts for MATLAB applications will be available via the Web. Exercises are given within the text to allow further practice with selected topics.

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 46,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489928467

Get Book

Nonlinear Partial Differential Equations for Scientists and Engineers by Lokenath Debnath Pdf

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.

Author : Alex Kasman
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 40,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821852453

Get Book

Glimpses of Soliton Theory by Alex Kasman Pdf

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. --

Author : Claire David,Zhaosheng Feng
Publisher : Bentham Science Publishers
Page : 267 pages
File Size : 52,6 Mb
Release : 2010
Category : Science
ISBN : 9781608051403

Get Book

Solitary Waves in Fluid Media by Claire David,Zhaosheng Feng Pdf

Since the first description by John Scott Russel in 1834, the solitary wave phenomenon has attracted considerable interests from scientists. The most interesting discovery since then has been the ability to integrate most of the nonlinear wave equations which govern solitary waves, from the Korteweg-de Vries equation to the nonlinear Schrodinger equation, in the 1960's. From that moment, a huge amount of theoretical works can be found on solitary waves. Due to the fact that many physical phenomena can be described by a soliton model, applications have followed each other, in telecommunications

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 49,9 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

Get Book

Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Author : Michael Shearer,Rachel Levy
Publisher : Princeton University Press
Page : 286 pages
File Size : 46,5 Mb
Release : 2015-03-01
Category : Mathematics
ISBN : 9780691161297

Get Book

Partial Differential Equations by Michael Shearer,Rachel Levy Pdf

An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 44,6 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

Get Book

Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : Alparslan Gök, S?rma Zeynep,Aru?aslan Çinçin, Duygu
Publisher : IGI Global
Page : 284 pages
File Size : 45,9 Mb
Release : 2019-11-22
Category : Mathematics
ISBN : 9781799801368

Get Book

Emerging Applications of Differential Equations and Game Theory by Alparslan Gök, S?rma Zeynep,Aru?aslan Çinçin, Duygu Pdf

Branches of mathematics and advanced mathematical algorithms can help solve daily problems throughout various fields of applied sciences. Domains like economics, mechanical engineering, and multi-person decision making benefit from the inclusion of mathematics to maximize utility and cooperation across disciplines. There is a need for studies seeking to understand the theories and practice of using differential mathematics to increase efficiency and order in the modern world. Emerging Applications of Differential Equations and Game Theory is a collection of innovative research that examines the recent advancements on interdisciplinary areas of applied mathematics. While highlighting topics such as artificial neuron networks, stochastic optimization, and dynamical systems, this publication is ideally designed for engineers, cryptologists, economists, computer scientists, business managers, mathematicians, mechanics, academicians, researchers, and students.

Author : Marcus Pivato
Publisher : Cambridge University Press
Page : 631 pages
File Size : 54,9 Mb
Release : 2010-01-07
Category : Mathematics
ISBN : 9780521199704

Get Book

Linear Partial Differential Equations and Fourier Theory by Marcus Pivato Pdf

This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.

Author : Peter D. Miller,Peter A. Perry,Jean-Claude Saut,Catherine Sulem
Publisher : Springer Nature
Page : 528 pages
File Size : 49,5 Mb
Release : 2019-11-14
Category : Mathematics
ISBN : 9781493998067

Get Book

Nonlinear Dispersive Partial Differential Equations and Inverse Scattering by Peter D. Miller,Peter A. Perry,Jean-Claude Saut,Catherine Sulem Pdf

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.

Author : Alexei Cheviakov
Publisher : Springer Nature
Page : 322 pages
File Size : 53,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031530746

Get Book

Analytical Properties of Nonlinear Partial Differential Equations by Alexei Cheviakov Pdf

Author : C. Eugene Wayne,Michael I. Weinstein
Publisher : Springer
Page : 79 pages
File Size : 41,7 Mb
Release : 2015-08-08
Category : Mathematics
ISBN : 9783319199351

Get Book

Dynamics of Partial Differential Equations by C. Eugene Wayne,Michael I. Weinstein Pdf

This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.