Traveling Wave Solutions for Nonlinear Partial Differential Equations
Author : Hinwa Leung
Publisher :
Page : 176 pages
File Size : 40,99 MB
Release : 1994
Category : Differential equations, Nonlinear
ISBN :
Author : Hinwa Leung
Publisher :
Page : 176 pages
File Size : 40,99 MB
Release : 1994
Category : Differential equations, Nonlinear
ISBN :
Author : Graham Griffiths
Publisher : Academic Press
Page : 463 pages
File Size : 28,41 MB
Release : 2010-12-09
Category : Mathematics
ISBN : 0123846536
Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net Includes a spectrum of applications in science, engineering, applied mathematics Presents a combination of numerical and analytical methods Provides transportable computer codes in Matlab and Maple
Author : Mark J. Ablowitz
Publisher : Cambridge University Press
Page : 532 pages
File Size : 38,57 MB
Release : 1991-12-12
Category : Mathematics
ISBN : 0521387302
This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.
Author : Z.J. Yang
Publisher :
Page : 23 pages
File Size : 17,26 MB
Release : 2018
Category :
ISBN :
We have studied a series of (ansätze) ordinary differential equations of the first-order, which correspond to the travelling (and/or solitary) wave solutions of some nonlinear partial differential equations. We have investigated the conditions, under which the nonlinear partial differential equations have the certain kinds of travelling (and/or solitary) wave solutions. As a consequence of applications, we can take the trial procedures to obtain the travelling wave solutions, which is a very efficient method to solve several classes of nonlinear partial differential equations.
Author : Robin Stanley Johnson
Publisher : Cambridge University Press
Page : 468 pages
File Size : 45,33 MB
Release : 1997-10-28
Category : Mathematics
ISBN : 9780521598323
This text considers classical and modern problems in linear and non-linear water-wave theory.
Author : Carlo Cattani
Publisher : Walter de Gruyter GmbH & Co KG
Page : 392 pages
File Size : 19,79 MB
Release : 2015-01-01
Category : Mathematics
ISBN : 3110472090
The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications, theoretical and applied physics as quantum mechanics, signal analysis, and in those relevant research fields where nonlinear dynamics occurs and several tools of nonlinear analysis are required. Dynamical processes and dynamical systems of fractional order attract researchers from many areas of sciences and technologies, ranging from mathematics and physics to computer science.
Author : A. I. Volpert
Publisher : American Mathematical Soc.
Page : 474 pages
File Size : 42,20 MB
Release :
Category : Mathematics
ISBN : 9780821897577
The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Author : Inna Shingareva
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 29,75 MB
Release : 2011-07-24
Category : Mathematics
ISBN : 370910517X
The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).
Author : G. B. Whitham
Publisher : John Wiley & Sons
Page : 660 pages
File Size : 46,29 MB
Release : 2011-10-18
Category : Science
ISBN : 1118031202
Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms.
Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 30,6 MB
Release : 2010-05-28
Category : Mathematics
ISBN : 364200251X
"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.