"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.

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Nonlinear Physical Science: Partial Differential Equations And Solitary Wave Theory(chinese Edition)

偏微分方程与孤波理论 英文版

Abdul-MajidWazwaz著

Spektrum Akademischer Verlag. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Springer London, Limited

北京:高等教育出版社

Nonlinear physical science, Beijing, Dordrecht, 2009

Nonlinear physical science, Beijing : Berlin, ©2009

China, People's Republic, China

Springer Nature, Beijing, 2009

Germany, Germany

Aug 13, 2009

Mar 28, 2007

2009, 2010

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Source title: Partial Differential Equations and Solitary Waves Theory (Nonlinear Physical Science)

Source title: Nonlinear physical science: partial differential equations and solitary wave theory(Chinese Edition)

Bookmarks: p1 (p1): Part Ⅰ　Partial Differential Equations
p2 (p3): 1 Basic Concepts
p3 (p3): 1.1　Introduction
p4 (p4): 1.2　Definitions
p5 (p4): 1.2.1　Definition of a PDE
p6 (p5): 1.2.2 Order of a PDE
p7 (p6): 1.2.3　Linear and Nonlinear PDEs
p8 (p7): 1.2.4　Some Linear Partial Differential Equations
p9 (p7): 1.2.5 Some Nonlinear Partial Differential Equations
p10 (p9): 1.2.6　Homogeneous and Inhomogeneous PDEs
p11 (p9): 1.2.7 Solution of a PDE
p12 (p11): 1.2.8 Boundary Conditions
p13 (p12): 1.2.9 Initial Conditions
p14 (p12): 1.2.10　Well-posed PDEs
p15 (p14): 1.3 Classifications of a Second-order PDE
p16 (p17): References
p17 (p19): 2 First-order Partial Differential Equations
p18 (p19): 2.1　Introduction
p19 (p19): 2.2　Adomian Decomposition Method
p20 (p36): 2.3　The Noise Terms Phenomenon
p21 (p41): 2.4　The Modified Decomposition Method
p22 (p47): 2.5　The Variational Iteration Method
p23 (p54): 2.6　Method of Characteristics
p24 (p59): 2.7 Systems of Linear PDEs by Adomian Method
p25 (p63): 2.8 Systems of Linear PDEs by Variational Iteration Method
p26 (p68): References
p27 (p69): 3 One Dimensional Heat Flow
p28 (p69): 3.1 Introduction
p29 (p70): 3.2　The Adomian Decomposition Method
p30 (p73): 3.2.1　Homogeneous Heat Equations
p31 (p80): 3.2.2　Inhomogeneous Heat Equations
p32 (p83): 3.3　The Variational Iteration Method
p33 (p84): 3.3.1　Homogeneous Heat Equations
p34 (p87): 3.3.2　Inhomogeneous Heat Equations
p35 (p89): 3.4　Method of Separation of Variables
p36 (p89): 3.4.1 Analysis of the Method
p37 (p99): 3.4.2　Inhomogeneous Boundary Conditions
p38 (p102): 3.4.3 Equations with Lateral Heat Loss
p39 (p106): References
p40 (p107): 4　Higher Dimensional Heat Flow
p41 (p107): 4.1　Introduction
p42 (p108): 4.2　Adomian Decomposition Method
p43 (p108): 4.2.1　Two Dimensional Heat Flow
p44 (p116): 4.2.2　Three Dimensional Heat Flow
p45 (p124): 4.3　Method of Separation of Variables
p46 (p124): 4.3.1　Two Dimensional Heat Flow
p47 (p134): 4.3.2　Three Dimensional Heat Flow
p48 (p140): References
p49 (p143): 5 One Dimensional Wave Equation
p50 (p143): 5.1 Introduction
p51 (p144): 5.2　Adornian Decomposition Method
p52 (p146): 5.2.1　Homogeneous Wave Equations
p53 (p152): 5.2.2 Inhomogeneous Wave Equations
p54 (p157): 5.2.3 Wave Equation in an Infinite Domain
p55 (p162): 5.3　The Variational Iteration Method
p56 (p162): 5.3.1　Homogeneous Wave Equations
p57 (p168): 5.3.2 Inhomogeneous Wave Equations
p58 (p170): 5.3.3　Wave Equation in an Infinite Domain
p59 (p174): 5.4 Method of Separation of Variables
p60 (p174): 5.4.1 Analysis of the Method
p61 (p184): 5.4.2 Inhomogeneous Boundary Conditions
p62 (p190): 5.5　Wave Equation in an Infinite Domain:D'Alembert Solution
p63 (p194): References
p64 (p195): 6　Higher Dimensional Wave Equation
p65 (p195): 6.1　Introduction
p66 (p195): 6.2 Adomian Decomposition Method
p67 (p196): 6.2.1 Two Dimensional Wave Equation
p68 (p210): 6.2.2 Three Dimensional Wave Equation
p69 (p220): 6.3　Method of Separation of Variables
p70 (p221): 6.3.1　Two Dimensional Wave Equation
p71 (p231): 6.3.2　Three Dimensional Wave Equation
p72 (p236): References
p73 (p237): 7　Laplace's Equation
p74 (p237): 7.1　Introduction
p75 (p238): 7.2　Adomian Decomposition Method
p76 (p238): 7.2.1　Two Dimensional Laplace's Equation
p77 (p247): 7.3　The Variational Iteration Method
p78 (p251): 7.4　Method of Separation of Variables
p79 (p251): 7.4.1　Laplace's Equation in Two Dimensions
p80 (p259): 7.4.2　Laplace's Equation in Three Dimensions
p81 (p267): 7.5　Laplace's Equation in Polar Coordinates
p82 (p268): 7.5.1　Laplace's Equation for a Disc
p83 (p275): 7.5.2　Laplace's Equation for an Annulus
p84 (p283): References
p85 (p285): 8 Nonlinear Partial Differential Equations
p86 (p285): 8.1　Introduction
p87 (p287): 8.2　Adomian Decomposition Method
p88 (p288): 8.2.1 Calculation of Adomian Polynomials
p89 (p292): 8.2.2　Alternative Algorithm for Calculating Adomian Polynomials
p90 (p301): 8.3 Nonlinear ODEs by Adomian Method
p91 (p312): 8.4 Nonlinear ODEs by VIM
p92 (p319): 8.5 Nonlinear PDEs by Adomian Method
p93 (p334): 8.6　Nonlinear PDEs by VIM
p94 (p341): 8.7　Nonlinear PDEs Systems by Adomian Method
p95 (p347): 8.8 Systems of Nonlinear PDEs by VIM
p96 (p351): References
p97 (p353): 9　Linear and Nonlinear Physical Models
p98 (p353): 9.1 Introduction
p99 (p354): 9.2　The Nonlinear Advection Problem
p100 (p360): 9.3　The Goursat Problem
p101 (p370): 9.4 The Klein-Gordon Equation
p102 (p371): 9.4.1　Linear Klein-Gordon Equation
p103 (p375): 9.4.2 Nonlinear Klein-Gordon Equation
p104 (p378): 9.4.3 The Sine-Gordon Equation
p105 (p381): 9.5　The Burgers Equation
p106 (p388): 9.6　The Telegraph Equation
p107 (p394): 9.7 Schrodinger Equation
p108 (p394): 9.7.1 The Linear Schrodinger Equation
p109 (p397): 9.7.2　The Nonlinear Schrodinger Equation
p110 (p401): 9.8　Korteweg-de Vries Equation
p111 (p405): 9.9　Fourth-order Parabolic Equation
p112 (p405): 9.9.1　Equations with Constant Coefficients
p113 (p408): 9.9.2　Equations with Variable Coefficients
p114 (p413): References
p115 (p415): 10 Numerical Applications and Padé Approximants
p116 (p415): 10.1　Introduction
p117 (p416): 10.2　Ordinary Differential Equations
p118 (p416): 10.2.1　Perturbation Problems
p119 (p421): 10.2.2　Nonperturbed Problems
p120 (p427): 10.3　Partial Differential Equations
p121 (p430): 10.4　The Padé Approximants
p122 (p439): 10.5　Padé Approximants and Boundary Value Problems
p123 (p455): References
p124 (p457): 11 Solitons and Compactons
p125 (p457): 11.1　Introduction
p126 (p459): 11.2　Solitons
p127 (p460): 11.2.1　The KdV Equation
p128 (p462): 11.2.2　The Modified KdV Equation
p129 (p464): 11.2.3　The Generalized KdV Equation
p130 (p464): 11.2.4　The Sine-Gordon Equation
p131 (p465): 11.2.5　The Boussinesq Equation
p132 (p467): 11.2.6　The Kadomtsev-Petviashvili Equation
p133 (p469): 11.3　Compactons
p134 (p474): 11.4　The Defocusing Branch of K(n,n)
p135 (p475): References
p136 (p479): Part Ⅱ　Solitray Waves Theory
p137 (p479): 12 Solitary Waves Theory
p138 (p479): 12.1 Introduction
p139 (p480): 12.2　Definitions
p140 (p482): 12.2.1　Dispersion and Dissipation
p141 (p484): 12.2.2　Types of Travelling Wave Solutions
p142 (p490): 12.2.3 Nonanalytic Solitary Wave Solutions
p143 (p491): 12.3 Analysis of the Methods
p144 (p491): 12.3.1　The Tanh-coth Method
p145 (p493): 12.3.2　The Sine-cosine Method
p146 (p494): 12.3.3　Hirota's Bilinear Method
p147 (p496): 12.4　Conservation Laws
p148 (p502): References
p149 (p503): 13　The Family of the KdV Equations
p150 (p503): 13.1　Introduction
p151 (p505): 13.2　The Family of the KdV Equations
p152 (p505): 13.2.1　Third-order KdV Equations
p153 (p507): 13.2.2　The K(n,n) Equation
p154 (p507): 13.3　The KdV Equation
p155 (p508): 13.3.1 Using the Tanh-coth Method
p156 (p510): 13.3.2　Using the Sine-cosine Method
p157 (p510): 13.3.3 Multiple-soliton Solutions of the KdV Equation
p158 (p518): 13.4　The Modified KdV Equation
p159 (p519): 13.4.1 Using the Tanh-coth Method
p160 (p520): 13.4.2　Using the Sine-cosine Method
p161 (p521): 13.4.3 Multiple-soliton Solutions of the mKdV Equation
p162 (p523): 13.5 Singular Soliton Solutions
p163 (p526): 13.6　The Generalized KdV Equation
p164 (p526): 13.6.1 Using the Tanh-coth Method
p165 (p528): 13.6.2　Using the Sine-cosine Method
p166 (p528): 13.7　The Potential KdV Equation
p167 (p529): 13.7.1 Using the Tanh-coth Method
p168 (p533): 13.7.2 Multiple-soliton Solutions of the Potential KdV Equation……531 13.8　The Gardner Equation
p169 (p533): 13.8.1　The Kink Solution
p170 (p534): 13.8.2　The Soliton Solution
p171 (p535): 13.8.3　N-soliton Solutions of the Positive Gardner Equation
p172 (p537): 13.8.4　Singular Soliton Solutions
p173 (p542): 13.9 Generalized KdV Equation with Two Power Nonlinearities
p174 (p543): 13.9.1 Using the Tanh Method
p175 (p544): 13.9.2　Using the Sine-cosine Method
p176 (p544): 13.10　Compactons:Solitons with Compact Support
p177 (p546): 13.10.1 The K(n,n)Equation
p178 (p547): 13.11 Variants of the K(n,n) Equation
p179 (p548): 13.11.1 First Variant
p180 (p549): 13.11.2 Second Variant
p181 (p551): 13.11.3　Third Variant
p182 (p553): 13.12 Compacton-like Solutions
p183 (p553): 13.12.1 The Modified KdV Equation
p184 (p554): 13.12.2 The Gardner Equation
p185 (p554): 13.12.3 The Modified Equal Width Equation
p186 (p555): References
p187 (p557): 14 KdV and mKdV Equations of Higher-orders
p188 (p557): 14.1　Introduction
p189 (p558): 14.2　Family of Higher-order KdV Equations
p190 (p558): 14.2.1　Fifth-order KdV Equations
p191 (p561): 14.2.2　Seventh-order KdV Equations
p192 (p562): 14.2.3　Ninth-order KdV Equations
p193 (p562): 14.3 Fifth-order KdV Equations
p194 (p563): 14.3.1　Using the Tanh-coth Method
p195 (p564): 14.3.2　The First Condition
p196 (p566): 14.3.3　The Second Condition
p197 (p567): 14.3.4　N-soliton Solutions of the Fifth-order KdV Equations
p198 (p576): 14.4　Seventh-order KdV Equations
p199 (p576): 14.4.1　Using the Tanh-coth Method
p200 (p578): 14.4.2 N-soliton Solutions of the Seventh-order KdV Equations
p201 (p582): 14.5　Ninth-order KdV Equations
p202 (p583): 14.5.1 Using the Tanh-coth Method
p203 (p584): 14.5.2　The Soliton Solutions
p204 (p585): 14.6　Family of Higher-order mKdV Equations
p205 (p586): 14.6.1 N-soliton Solutions for Fifth-order mKdV Equation
p206 (p587): 14.6.2 Singular Soliton Solutions for Fifth-order mKdV Equation
p207 (p589): 14.6.3 N-soliton Solutions for the Seventh-order mKdV Equation
p208 (p591): 14.7 Complex Solution for the Seventh-order mKdV Equations
p209 (p592): 14.8　The Hirota-Satsuma Equations
p210 (p593): 14.8.1 Using the Tanh-coth Method
p211 (p594): 14.8.2　N-soliton Solutions of the Hirota-Satsuma System
p212 (p596): 14.8.3 N-soliton Solutions by an Alternative Method
p213 (p597): 14.9　Generalized Short Wave Equation
p214 (p602): References
p215 (p605): 15　Family of KdV-type Equations
p216 (p605): 15.1 Introduction
p217 (p606): 15.2　The Complex Modified KdV Equation
p218 (p607): 15.2.1 Using the Sine-cosine Method
p219 (p608): 15.2.2　Using the Tanh-coth Method
p220 (p612): 15.3 The Benjamin-Bona-Mahony Equation
p221 (p612): 15.3.1 Using the Sine-cosine Method
p222 (p613): 15.3.2　Using the Tanh-coth Method
p223 (p615): 15.4　The Medium Equal Width(MEW)Equation
p224 (p615): 15.4.1 Using the Sine-cosine Method
p225 (p616): 15.4.2　Using the Tanh-coth Method
p226 (p617): 15.5　The Kawahara and the Modified Kawahara Equations
p227 (p618): 15.5.1　The Kawahara Equation
p228 (p619): 15.5.2　The Modified Kawahara Equation
p229 (p620): 15.6　The Kadomtsev-Petviashvili(KP)Equation
p230 (p621): 15.6.1 Using the Tanh-coth Method
p231 (p622): 15.6.2 Multiple-soliton Solutions of the KP Equation
p232 (p626): 15.7　The Zakharov-Kuznetsov(ZK)Equation
p233 (p629): 15.8 The Benjamin-Ono Equation
p234 (p630): 15.9　The KdV-Burgers Equation
p235 (p632): 15.10 Seventh-order KdV Equation
p236 (p632): 15.10.1　The Sech Method
p237 (p634): 15.11 Ninth-order KdV Equation
p238 (p634): 15.11.1　The Sech Method
p239 (p637): References
p240 (p639): 16 Boussinesq,Klein-Gordon and Liouville Equations
p241 (p639): 16.1 Introduction
p242 (p641): 16.2　The Boussinesq Equation
p243 (p641): 16.2.1 Using the Tanh-coth Method
p244 (p643): 16.2.2 Multiple-soliton Solutions of the Boussinesq Equation
p245 (p646): 16.3　The Improved Boussinesq Equation
p246 (p648): 16.4　The Klein-Gordon Equation
p247 (p649): 16.5 The Liouville Equation
p248 (p651): 16.6　The Sine-Gordon Equation
p249 (p651): 16.6.1 Using the Tanh-coth Method
p250 (p654): 16.6.2　Using the B？cklund Transformation
p251 (p655): 16.6.3 Multiple-soliton Solutions for Sine-Gordon Equation
p252 (p657): 16.7　The Sinh-Gordon Equation
p253 (p658): 16.8 The Dodd-Bullough-Mikhailov Equation
p254 (p659): 16.9　The Tzitzeica-Dodd-Bullough Equation
p255 (p661): 16.10 The Zhiber-Shabat Equation
p256 (p662): References
p257 (p665): 17 Burgers,Fisher and Related Equations
p258 (p665): 17.1　Introduction
p259 (p666): 17.2　The Burgers Equation
p260 (p667): 17.2.1　Using the Tanh-coth Method
p261 (p668): 17.2.2　Using the Cole-Hopf Transformation
p262 (p670): 17.3　The Fisher Equation
p263 (p671): 17.4　The Huxley Equation
p264 (p673): 17.5　The Burgers-Fisher Equation
p265 (p673): 17.6　The Burgers-Huxley Equation
p266 (p675): 17.7　The FitzHugh-Nagumo Equation
p267 (p676): 17.8　Parabolic Equation with Exponential Nonlinearity
p268 (p678): 17.9　The Coupled Burgers Equation
p269 (p680): 17.10　The Kuramoto-Sivashinsky(KS)Equation
p270 (p681): References
p271 (p683): 18 Families of Camassa-Holm and Schrodinger Equations
p272 (p683): 18.1　Introduction
p273 (p686): 18.2　The Family of Camassa-Holm Equations
p274 (p686): 18.2.1　Using the Tanh-coth Method
p275 (p688): 18.2.2　Using an Exponential Algorithm
p276 (p689): 18.3 Schrodinger Equation of Cubic Nonlinearity
p277 (p690): 18.4 Schrodinger Equation with Power Law Nonlinearity
p278 (p692): 18.5　The Ginzburg-Landau Equation
p279 (p693): 18.5.1 The Cubic Ginzburg-Landau Equation
p280 (p694): 18.5.2　The Generalized Cubic Ginzburg-Landau Equation
p281 (p695): 18.5.3　The Generalized Quintic Ginzburg-Landau Equation
p282 (p696): References
p283 (p699): Appendix
p284 (p699): A Indefinite Integrals
p285 (p699): A.1 Fundamental Forms
p286 (p700): A.2　Trigonometric Forms
p287 (p700): A.3 Inverse Trigonometric Forms
p288 (p701): A.4 Exponential and Logarithmic Forms
p289 (p701): A.5　Hyperbolic Forms
p290 (p702): A.6 Other Forms
p291 (p703): B Series
p292 (p703): B.1 Exponential Functions
p293 (p703): B.2 Trigonometric Functions
p294 (p704): B.3 Inverse Trigonometric Functions
p295 (p704): B.4　Hyperbolic Functions
p296 (p704): B.5 Inverse Hyperbolic Functions
p297 (p705): C　Exact Solutions of Burgers' Equation
p298 (p707): D Padé Approximants for Well-Known Functions
p299 (p707): D.1 Exponential Functions
p300 (p707): D.2 Trigonometric Functions
p301 (p709): D.3　Hyperbolic Functions
p302 (p709): D.4　Logarithmic Functions
p303 (p711): E　The Error and Gamma Functions
p304 (p711): E.1　The Error function
p305 (p711): E.2 The Gamma function Г（x）
p306 (p712): F Infinite Series
p307 (p712): F.1 Numerical Series
p308 (p713): F.2 Trigonometric Series
p309 (p715): Answers
p310 (p739): Index

2024-06-13