Homotopy Based Methods In Water Engineering

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Homotopy-Based Methods in Water Engineering

Manotosh Kumbhakar,Vijay P. Singh
Homotopy Based Methods in Water Engineering Book PDF

Author : Manotosh Kumbhakar,Vijay P. Singh
Publisher : CRC Press
Page : 471 pages
File Size : 41,9 Mb
Release : 2023-07-20
Category : Technology & Engineering
ISBN : 9781000893359

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Homotopy-Based Methods in Water Engineering by Manotosh Kumbhakar,Vijay P. Singh Pdf

Most complex physical phenomena can be described by nonlinear equations, specifically, differential equations. In water engineering, nonlinear differential equations play a vital role in modeling physical processes. Analytical solutions to strong nonlinear problems are not easily tractable, and existing techniques are problem-specific and applicable for specific types of equations. Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), systems of PDEs, and integro-differential equations using the homotopy-based methods. The content of the book deals with some selected problems of hydraulics of open-channel flow (with or without sediment transport), groundwater hydrology, surface-water hydrology, general Burger’s equation, and water quality. Features: Provides analytical treatments to some key problems in water engineering Describes the applicability of homotopy-based methods for solving nonlinear equations, particularly differential equations Compares different approaches in dealing with issues of nonlinearity

Introduction to Numerical Methods for Water Resources

W. L. Wood
Introduction to Numerical Methods for Water Resources Book PDF

Author : W. L. Wood
Publisher : Oxford University Press
Page : 290 pages
File Size : 48,7 Mb
Release : 1993
Category : Mathematics
ISBN : 0198596901

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Introduction to Numerical Methods for Water Resources by W. L. Wood Pdf

Numerical methods provide a powerful and essential tool for the solution of problems of water resources. This book gives an elementary introduction to the various methods in current use and demonstrates that different methods work well in different situations and some problems requirecombinations of methods. It is essential to know something of all of them in order to make a reasoned judgement of current practice. Their applications are discussed and more specialised versions are outlined along with many references making this an invaluable, comprehensive coverage of thefield.

Beyond Perturbation

Shijun Liao
Beyond Perturbation Book PDF

Author : Shijun Liao
Publisher : CRC Press
Page : 335 pages
File Size : 48,6 Mb
Release : 2003-10-27
Category : Mathematics
ISBN : 9781135438296

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Beyond Perturbation by Shijun Liao Pdf

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.

Advances In Engineering Mechanics--reflections And Outlooks: In Honor Of Theodore Y-t Wu

Daniel T Valentine,Michelle H Teng,Allen T Chwang
Advances In Engineering Mechanics reflections And Outlooks In Honor Of Theodore Y t Wu Book PDF

Author : Daniel T Valentine,Michelle H Teng,Allen T Chwang
Publisher : World Scientific
Page : 748 pages
File Size : 49,8 Mb
Release : 2005-11-29
Category : Science
ISBN : 9789814481052

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Advances In Engineering Mechanics--reflections And Outlooks: In Honor Of Theodore Y-t Wu by Daniel T Valentine,Michelle H Teng,Allen T Chwang Pdf

This volume presents more than 40 original papers on recent advances in several topics in engineering mechanics presented at The Theodore Y-T Wu Symposium on Engineering Mechanics: A celebration of Professor Wu's scientific contributions for his 80th birthday. The distinguished contributors include several members of the National Academy of Engineers and the topics cover nonlinear water waves, swimming and flying in nature, biomechanics, data analysis methodology, and propulsion hydrodynamics.The papers honor the significant accomplishments of Professor Wu in Engineering Science at Caltech, particularly in the areas of nonlinear waves, hydrodynamics, biomechanics and wave-structure interaction. They review the present state of the art of engineering mechanics, and chart the future of the field from the viewpoint of civil engineering, biomechanics, geophysics, mechanical engineering, naval architecture, ocean, and offshore engineering. The primary purpose of this book is to provide guidance and inspiration for those interested in continuing to advance engineering mechanics into the 21st century. To quote Professor Wu: ”The value of a book publication lies in disseminating new knowledge attained with effort and dedication from all those who participate, and in having the useful results within ready reach of students and researchers actively working in the field.”

Encyclopedia of Ocean Engineering

Weicheng Cui,Shixiao Fu,Zhiqiang Hu
Encyclopedia of Ocean Engineering Book PDF

Author : Weicheng Cui,Shixiao Fu,Zhiqiang Hu
Publisher : Springer Nature
Page : 2203 pages
File Size : 53,8 Mb
Release : 2022-06-29
Category : Technology & Engineering
ISBN : 9789811069468

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Encyclopedia of Ocean Engineering by Weicheng Cui,Shixiao Fu,Zhiqiang Hu Pdf

This encyclopedia adopts a wider definition for the concept of ocean engineering. Specifically, it includes (1) offshore engineering: fixed and floating offshore oil and gas platforms; pipelines and risers; cables and moorings; buoy technology; foundation engineering; ocean mining; marine and offshore renewable energy; aquaculture engineering; and subsea engineering; (2) naval architecture: ship and special marine vehicle design; intact and damaged stability; technology for energy efficiency and green shipping; ship production technology; decommissioning and recycling; (3) polar and Arctic Engineering: ice mechanics; ice-structure interaction; polar operations; polar design; environmental protection; (4) underwater technologies: AUV/ROV design; AUV/ROV hydrodynamics; maneuvering and control; and underwater-specific communicating and sensing systems for AUV/ROVs. It summarizes the A–Z of the background and application knowledge of ocean engineering for use by ocean scientists and ocean engineers as well as nonspecialists such as engineers and scientists from all disciplines, economists, students, and politicians. Ocean engineering theories, ocean devices and equipment, ocean design and operation technologies are described by international experts, many from industry and each entry offers an introduction and references for further study, making current technology and operating practices available for future generations to learn from. The book also furthers our understanding of the current state of the art, leading to new and more efficient technologies with breakthroughs from new theory and materials. As the land resources approach the exploitation limit, ocean resources are becoming the next choice for the sustainable development. As such, ocean engineering is vital in the 21st century.

Homotopy Analysis Method in Nonlinear Differential Equations

Shijun Liao
Homotopy Analysis Method in Nonlinear Differential Equations Book PDF

Author : Shijun Liao
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 44,7 Mb
Release : 2012-06-22
Category : Mathematics
ISBN : 9783642251320

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Homotopy Analysis Method in Nonlinear Differential Equations by Shijun Liao Pdf

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

Wave Dynamics

Snehashish Chakraverty,Perumandla Karunakar
Wave Dynamics Book PDF

Author : Snehashish Chakraverty,Perumandla Karunakar
Publisher : World Scientific
Page : 297 pages
File Size : 40,7 Mb
Release : 2022-01-27
Category : Technology & Engineering
ISBN : 9789811245374

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Wave Dynamics by Snehashish Chakraverty,Perumandla Karunakar Pdf

There are various types of waves including water, sound, electromagnetic, seismic and shock etc. These waves need to be analyzed and understood for different practical applications. This book is an attempt to consider the waves in detail to understand the physical and mathematical phenomena. A major challenge is to model waves by experimental studies.The aim of this book is to address the efficient and recently developed theories along with the basic equations of wave dynamics. The latest development of analytical/semi analytical and numerical methods with respect to wave dynamics are also covered. Further few challenging experimental studies are considered for related problems. This book presents advances in wave dynamics in simple and easy to follow chapters for the benefit of the readers/researchers.

Mathematical Methods in Interdisciplinary Sciences

Snehashish Chakraverty
Mathematical Methods in Interdisciplinary Sciences Book PDF

Author : Snehashish Chakraverty
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 46,8 Mb
Release : 2020-07-15
Category : Mathematics
ISBN : 9781119585503

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Mathematical Methods in Interdisciplinary Sciences by Snehashish Chakraverty Pdf

Brings mathematics to bear on your real-world, scientific problems Mathematical Methods in Interdisciplinary Sciences provides a practical and usable framework for bringing a mathematical approach to modelling real-life scientific and technological problems. The collection of chapters Dr. Snehashish Chakraverty has provided describe in detail how to bring mathematics, statistics, and computational methods to the fore to solve even the most stubborn problems involving the intersection of multiple fields of study. Graduate students, postgraduate students, researchers, and professors will all benefit significantly from the author's clear approach to applied mathematics. The book covers a wide range of interdisciplinary topics in which mathematics can be brought to bear on challenging problems requiring creative solutions. Subjects include: Structural static and vibration problems Heat conduction and diffusion problems Fluid dynamics problems The book also covers topics as diverse as soft computing and machine intelligence. It concludes with examinations of various fields of application, like infectious diseases, autonomous car and monotone inclusion problems.

Advances in the Homotopy Analysis Method

Shijun Liao
Advances in the Homotopy Analysis Method Book PDF

Author : Shijun Liao
Publisher : World Scientific
Page : 428 pages
File Size : 46,8 Mb
Release : 2013-11-26
Category : Mathematics
ISBN : 9789814551267

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Advances in the Homotopy Analysis Method by Shijun Liao Pdf

Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity. This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications. Contents:Chance and Challenge: A Brief Review of Homotopy Analysis Method (S-J Liao)Predictor Homotopy Analysis Method (PHAM) (S Abbasbandy and E Shivanian)Spectral Homotopy Analysis Method for Nonlinear Boundary Value Problems (S Motsa and P Sibanda)Stability of Auxiliary Linear Operator and Convergence-Control Parameter (R A Van Gorder)A Convergence Condition of the Homotopy Analysis Method (M Turkyilmazoglu)Homotopy Analysis Method for Some Boundary Layer Flows of Nanofluids (T Hayat and M Mustafa)Homotopy Analysis Method for Fractional Swift–Hohenberg Equation (S Das and K Vishal)HAM-Based Package NOPH for Periodic Oscillations of Nonlinear Dynamic Systems (Y-P Liu)HAM-Based Mathematica Package BVPh 2.0 for Nonlinear Boundary Value Problems (Y-L Zhao and S-J Liao) Readership: Graduate students and researchers in applied mathematics, physics, nonlinear mechanics, engineering and finance. Keywords:Analytic Approxiamtion Method;Nonlinear;Homotopy;Applied MathematicsKey Features:The method described in the book can overcome almost all restrictions of other analytic approximation method for nonlinear problemsThis book is the first in homotopy analysis method, covering the newest advances, contributed by many top experts in different fields

Recent Advances in Applications of Computational and Fuzzy Mathematics

Snehashish Chakraverty,Sanjeewa Perera
Recent Advances in Applications of Computational and Fuzzy Mathematics Book PDF

Author : Snehashish Chakraverty,Sanjeewa Perera
Publisher : Springer
Page : 178 pages
File Size : 48,8 Mb
Release : 2018-07-17
Category : Computers
ISBN : 9789811311536

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Recent Advances in Applications of Computational and Fuzzy Mathematics by Snehashish Chakraverty,Sanjeewa Perera Pdf

This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.

Analytical Methods for Nonlinear Oscillators and Solitary Waves

Chu-Hui He,Hamid M. Sedighi,Ji-Huan He,Yusry El-Dib,Dragan Marinkovic
Analytical Methods for Nonlinear Oscillators and Solitary Waves Book PDF

Author : Chu-Hui He,Hamid M. Sedighi,Ji-Huan He,Yusry El-Dib,Dragan Marinkovic
Publisher : Frontiers Media SA
Page : 132 pages
File Size : 51,9 Mb
Release : 2023-11-24
Category : Science
ISBN : 9782832539637

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Analytical Methods for Nonlinear Oscillators and Solitary Waves by Chu-Hui He,Hamid M. Sedighi,Ji-Huan He,Yusry El-Dib,Dragan Marinkovic Pdf

The most well-known analytical method is the perturbation method, which has led to the great discovery of Neptune in 1846, and since then mathematical prediction and empirical observation became two sides of a coin in physics. However, the perturbation method is based on the small parameter assumption, and the obtained solutions are valid only for weakly nonlinear equations, which have greatly limited their applications to modern physical problems. To overcome the shortcomings, many mathematicians and physicists have been extensively developing various technologies for several centuries, however, there is no universal method for all nonlinear problems, and mathematical prediction with remarkably high accuracy is still much needed for modern physics, for example, the solitary waves traveling along an unsmooth boundary, the low-frequency property of a harvesting energy device, the pull-in voltage in a micro-electromechanical system. Now various effective analytical methods have appeared in the open literature, e.g., the homotopy perturbation method and the variational iteration method. An analytical solution provides a fast insight into its physical properties of a practical problem, e.g., frequency-amplitude relation of a nonlinear oscillator, solitary wave in an optical fiber, pull-in instability of a microelectromechanical system, making mathematical prediction even more attractive in modern physics. Nonlinear physics has been developing into a new stage, where the fractal-fractional differential equations have to be adopted to describe more accurately discontinuous problems, and it becomes ever more difficult to find an analytical solution for such nonlinear problems, and the analytical methods for fractal-fractional differential equations have laid the foundations for nonlinear physics.

4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019)

Hemen Dutta,Zakia Hammouch,Hasan Bulut,Haci Mehmet Baskonus
4th International Conference on Computational Mathematics and Engineering Sciences CMES 2019 Book PDF

Author : Hemen Dutta,Zakia Hammouch,Hasan Bulut,Haci Mehmet Baskonus
Publisher : Springer Nature
Page : 332 pages
File Size : 49,6 Mb
Release : 2020-01-10
Category : Technology & Engineering
ISBN : 9783030391126

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4th International Conference on Computational Mathematics and Engineering Sciences (CMES-2019) by Hemen Dutta,Zakia Hammouch,Hasan Bulut,Haci Mehmet Baskonus Pdf

This book gathers original research papers presented at the 4th International Conference on Computational Mathematics and Engineering Sciences, held at Akdeniz University, Antalya, Turkey, on 20–22 April 2019. Focusing on computational methods in science, mathematical tools applied to engineering, mathematical modeling and new aspects of analysis, the book discusses the applications of mathematical modelling in areas such as health science, engineering, computer science, social science, and economics. It also describes a wide variety of analytical, computational, and numerical methods. The conference aimed to foster cooperation between students and researchers in the areas of computational mathematics and engineering sciences, and provide a platform for them to share significant research ideas. This book is a valuable resource for graduate students, researchers and educators interested in the mathematical tools and techniques required for solving various problems arising in science and engineering, and understanding new methods and uses of mathematical analysis.

Advanced Numerical and Semi-Analytical Methods for Differential Equations

Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Advanced Numerical and Semi Analytical Methods for Differential Equations Book PDF

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 52,6 Mb
Release : 2019-04-16
Category : Mathematics
ISBN : 9781119423423

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Advanced Numerical and Semi-Analytical Methods for Differential Equations by Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao Pdf

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Applications of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer

Mohsen Sheikholeslami,Davood Domairry Ganji
Applications of Semi Analytical Methods for Nanofluid Flow and Heat Transfer Book PDF

Author : Mohsen Sheikholeslami,Davood Domairry Ganji
Publisher : Elsevier
Page : 888 pages
File Size : 43,8 Mb
Release : 2018-01-02
Category : Science
ISBN : 9780128136768

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Applications of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer by Mohsen Sheikholeslami,Davood Domairry Ganji Pdf

Application of Semi-Analytical Methods for Nanofluid Flow and Heat Transfer applies semi-analytical methods to solve a range of engineering problems. After various methods are introduced, their application in nanofluid flow and heat transfer, magnetohydrodynamic flow, electrohydrodynamic flow and heat transfer, and nanofluid flow in porous media within several examples are explored. This is a valuable reference resource for materials scientists and engineers that will help familiarize them with a wide range of semi-analytical methods and how they are used in nanofluid flow and heat transfer. The book also includes case studies to illustrate how these methods are used in practice. Presents detailed information, giving readers a complete familiarity with governing equations where nanofluid is used as working fluid Provides the fundamentals of new analytical methods, applying them to applications of nanofluid flow and heat transfer in the presence of magnetic and electric field Gives a detailed overview of nanofluid motion in porous media

Partial Differential Equations and Solitary Waves Theory

Abdul-Majid Wazwaz
Partial Differential Equations and Solitary Waves Theory Book PDF

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 48,9 Mb
Release : 2010-05-28
Category : Mathematics
ISBN : 9783642002519

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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.