Partial Differential Equations and Solitary Waves Theory is a self-containedbook divided into two parts： Part I is a coherent survey bringing together newlydeveloped methods for solving PDEs. While some traditional techniques are pre-sented, this part does not require thorough understanding of abstract theories orcompact concepts. Well-selected worked examples and exercises shall guide thereader through the text. Part II provides an extensive exposition of the solitarywaves theory. This part handles nonlinear evolution equations by methods suchas Hirotas bilinear method or the tanh-coth method. A self-contained treatmentis presented to discuss complete integrability of a wide class of nonlinear equa-tions. This part presents in an accessible manner a systematic presentation ofsolitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons.

While the whole book can be used as a text for advanced undergraduate andgraduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineer-ing, and other related fields.

Part I Partial Differential Equations
  1 Basic Concepts
   1.1 Introduction
   1.2 Definitions
   1.3 Classifications of a Second-order PDE
   References
  2 First-order Partial Differential Equations
   2.1 Introduction
   2.2 Adomian Decomposition Method
   2.3 The Noise Terms Phenomenon
   2.4 The Modified Decomposition Method
   2.5 The Variational Iteration Method
   2.6 Method of Characteristics
   2.7 Systems of Linear PDEs by Adomian Method
   2.8 Systems of Linear PDEs by Variational Iteration Method
   References
  3 One Dimensional Heat Flow
   3.1 Introduction
   3.2 The Adomian Decomposition Method
   3.3 The Variational Iteration Method
   3.4 Method of Separation of Variables
   References
  4 Higher Dimensional Heat Flow
   4.1 Introduction
   4.2 Adomian Decomposition Method
   4.3 Method of Separation of Variables
   References
  5 One Dimensional Wave Equation
   5.1 Introduction
   5.2 Adomian Decomposition Method
   5.3 The Variational Iteration Method
   5.4 Method of Separation of Variables
   5.5 Wave Equation in an Infinite Domain: DAlembert Solution
   References
  6 Higher Dimensional Wave Equation
   6.1 Introduction
   6.2 Adomian Decomposition Method
   6.3 Method of Separation of Variables
   References
  7 Laplaces Equation
   7.1 Introduction
   7.2 Adomian Decomposition Method
   7.3 The Variational Iteration Method
   7.4 Method of Separation of Variables
   7.5 Laplaces Equation in Polar Coordinates
   References
  8 Nonlinear Partial Differential Equations
   8.1 Introduction
   8.2 Adomian Decomposition Method
   8.3 Nonlinear ODEs by Adomian Method
   8.4 Nonlinear ODEs by VIM
   8.5 Nonlinear PDEs by Adomian Method
   8.6 Nonlinear PDEs by VIM
   8.7 Nonlinear PDEs Systems by Adomian Method..
   8.8 Systems of Nonlinear PDEs by VIM
   References
  9 Linear and Nonlinear Physical Models
   9.1 Introduction
   9.2 The Nonlinear Advection Problem
   9.3 The Goursat Problem
   9.4 The Klein-Gordon Equation
   9.5 The Burgers Equation
   9.6 The Telegraph Equation
   9.7 Schrodinger Equation
   9.8 Korteweg-deVries Equation
   9.9 Fourth-order Parabolic Equation
   References
  10 Numerical Applications and Pade Approximants
   10.1 Introduction
   10.2 Ordinary Differential Equations
   10.3 Partial Differential Equations
   10.4 The Pade Approximants
   10.5 Pad6 Approximants and Boundary Value Problems
   References
  11 Solitons and Compaetons
   11.1 Introduction
   11.2 Solitons
   11.3 Compactons
   11.4 The Defocusing Branch of K(n,n)
   References
Part II Solitray Waves Theory
  12 Solitary Waves Theory
   12.1 Introduction
   12.2 Definitions
   12.3 Analysis of the Methods
   12.4 Conservation Laws
   References

非线性物理科学系列NPS