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Author : 黃冠傑
Publisher :
ISBN 13 :
Total Pages : 42 pages
Book Rating : 4.:/5 (18 download)
Download or read book Exact Traveling Wave Solutions for Some Nonlinear Systems written by 黃冠傑 and published by . This book was released on 2018 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carlo Cattani
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110472090
Total Pages : 392 pages
Book Rating : 4.1/5 (14 download)
Download or read book Fractional Dynamics written by Carlo Cattani and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-01-01 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : G. Adomian
Publisher : Springer Science & Business Media
ISBN 13 : 9401582890
Total Pages : 367 pages
Book Rating : 4.4/5 (15 download)
Download or read book Solving Frontier Problems of Physics: The Decomposition Method written by G. Adomian and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.
Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571668
Total Pages : 528 pages
Book Rating : 4.1/5 (15 download)
Download or read book Fractional Differential Equations written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Author : Z.J. Yang
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (13 download)
Download or read book Travelling Wave Solutions to Nonlinear Evolution and Wave Equations written by Z.J. Yang and published by . This book was released on 2018 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Lokenath Debnath
Publisher : Springer Science & Business Media
ISBN 13 : 1489928464
Total Pages : 602 pages
Book Rating : 4.4/5 (899 download)
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.
Author : Yong Liu
Publisher : Springer Nature
ISBN 13 : 3030324567
Total Pages : 1004 pages
Book Rating : 4.0/5 (33 download)
Download or read book Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery written by Yong Liu and published by Springer Nature. This book was released on 2019-11-06 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the recent advances in natural computation, fuzzy systems and knowledge discovery. Presenting selected, peer-reviewed papers from the 15th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019), held in Kunming, China, from 20 to 22 July 2019, it is a useful resource for researchers, including professors and graduate students, as well as R&D staff in industry.
Author : Vladimir B. Matveev
Publisher : Springer
ISBN 13 : 9783662009246
Total Pages : 122 pages
Book Rating : 4.0/5 (92 download)
Download or read book Darboux Transformations and Solitons written by Vladimir B. Matveev and published by Springer. This book was released on 1992-09-30 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modem theory of solitons was born in 1967 when Gardner, Greene, Kruskal and Miura related the solution of the Cauchy initial value problem for the Korteweg-de Vries equation to the inverse scattering problem for a one dimensional linear Schrödinger equation. Soliton theory is now a large part of theoretical and mathematical physics. An important method used to solve related equations is based on the Inverse Scattering Transform (IST). This IST method has been extended and applied to a large variety of (analytically) solvable non linear evolution equations, including many important examples describing phe nomena in nonlinear optics, solid state physics, hydrodynamics, theory of general relativity, plasma physics, etc. In the about twenty years of development the necessary mathematical tools have become rather sophisticated. They include the methods of algebraic geome try, the machinery of group representations, the theory of the local and nonlocal Riemann-Hilbert problem and many other "higher" levels of contemporary math ematics.
Author : Hinwa Leung
Publisher :
ISBN 13 :
Total Pages : 176 pages
Book Rating : 4.:/5 (321 download)
Download or read book Traveling Wave Solutions for Nonlinear Partial Differential Equations written by Hinwa Leung and published by . This book was released on 1994 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 364200251X
Total Pages : 700 pages
Book Rating : 4.6/5 (42 download)
Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 : Aizik I.. Volpert
Publisher : American Mathematical Soc.
ISBN 13 : 9780821811436
Total Pages : 448 pages
Book Rating : 4.8/5 (114 download)
Download or read book Traveling Wave Solutions of Parabolic Systems written by Aizik I.. Volpert and published by American Mathematical Soc.. This book was released on 2000 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of traveling 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. The main part of the book contains original approaches developed by the authors. Among these are a description of the long-term behavior of the solutions by systems of waves; construction of rotations of vector fields for noncompact operators describing wave solutions; a proof of the existence of waves by the Leray-Schauder method; local, global, and nonlinear stability analyses for some classes of systems; and a determination of the wave velocity by the minimax method and the method of successive approximations.The authors show that wide classes of reaction-diffusion systems can be reduced to so-called monotone and locally monotone systems. This fundamental result allows them to apply the theory to combustion and chemical kinetics. With introductory material accessible to nonmathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.
Author : Graham Griffiths
Publisher : Academic Press
ISBN 13 : 0123846536
Total Pages : 463 pages
Book Rating : 4.1/5 (238 download)
Download or read book Traveling Wave Analysis of Partial Differential Equations written by Graham Griffiths and published by Academic Press. This book was released on 2010-12-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : P.L. Sachdev
Publisher : CRC Press
ISBN 13 : 1000611418
Total Pages : 172 pages
Book Rating : 4.0/5 (6 download)
Download or read book Self-Similarity and Beyond written by P.L. Sachdev and published by CRC Press. This book was released on 2019-06-13 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out. Self-Similarity and Beyond presents
Author : Vasile Marinca
Publisher : Springer
ISBN 13 : 3319153749
Total Pages : 476 pages
Book Rating : 4.3/5 (191 download)
Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Author : Jaime Angulo Pava
Publisher : American Mathematical Soc.
ISBN 13 : 0821848976
Total Pages : 272 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1135440816
Total Pages : 835 pages
Book Rating : 4.1/5 (354 download)
Download or read book Handbook of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2004-06-02 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
Author : L. V. Ovsiannikov
Publisher : Academic Press
ISBN 13 : 1483219062
Total Pages : 433 pages
Book Rating : 4.4/5 (832 download)
Download or read book Group Analysis of Differential Equations written by L. V. Ovsiannikov and published by Academic Press. This book was released on 2014-05-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.
