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Handbook of Nonlinear Partial Differential Equations, 2nd Edition

Title: Handbook of Nonlinear Partial Differential Equations, 2nd Edition
Author: Andrei D. Polyanin, Valentin F. Zaitsev
ISBN: 1420087231 / 9781420087239
Format: Hard Cover
Pages: 1912
Publisher: CHAPMAN & HALL
Year: 2011
Availability: Out of Stock

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New to the Second Edition

  • More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions
  • Parabolic, hyperbolic, elliptic, and other systems of equations with solutions
  • Some exact methods and transformations
  • Symbolic and numerical methods for solving nonlinear PDEs with Maple™, Mathematica®, and MATLAB®
  • Many new illustrative examples and tables
  • A large list of references consisting of over 1,300 sources

To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.

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Part I : Exact Solutions of Nonlinear Partial Differential Equations
Chapter 1 : First-Order Quasilinear Equations
Chapter 2 : First-Order Equations with Two Independent Variables Quadratic in Derivatives
Chapter 3 : First-Order Nonlinear Equations with Two Independent Variables of General Form
Chapter 4 : First-Order Nonlinear Equations with Three or More Independent Variables
Chapter 5 : Second-Order Parabolic Equations with One Space Variable
Chapter 6 : Second-Order Parabolic Equations with Two or More Space Variables
Chapter 7 : Second-Order Hyperbolic Equations with One Space Variable
Chapter 8 : Second-Order Hyperbolic Equations with Two or More Space Variables
Chapter 9 : Second-Order Elliptic Equations with Two Space Variables
Chapter 10 : Second-Order Elliptic Equations with Three or More Space Variables
Chapter 11 : Second-Order Equations Involving Mixed Derivatives and Some Other Equations
Chapter 12 : Second-Order Equations of General Form
Chapter 13 : Third-Order Equations
Chapter 14 : Fourth-Order Equations
Chapter 15 : Equations of Higher Orders
Chapter 16 : Systems of Two First-Order Partial Differential Equations
Chapter 17 : Systems of Two Parabolic Equations
Chapter 18 : Systems of Two Second-Order Klein–Gordon Type Hyperbolic Equations
Chapter 19 : Systems of Two Elliptic Equations
Chapter 20 : First-Order Hydrodynamic and Other Systems Involving Three or More Equations
Chapter 21 : Navier–Stokes and Related Equations
Chapter 22 : Systems of General Form

Part II : Exact Methods for Nonlinear Partial Differential Equations
Chapter 23 : Methods for Solving First-Order Quasilinear Equations
Chapter 24 : Methods for Solving First-Order Nonlinear Equations
Chapter 25 : Classification of Second-Order Nonlinear Equations
Chapter 26 : Transformations of Equations of Mathematical Physics
Chapter 27 : Traveling-Wave Solutions and Self-Similar Solutions
Chapter 28 : Elementary Theory of Using Invariants for Solving Equations
Chapter 29 : Method of Generalized Separation of Variables
Chapter 30 : Method of Functional Separation of Variables
Chapter 31 : Direct Method of Symmetry Reductions of Nonlinear Equations
Chapter 32 : Classical Method of Symmetry Reductions
Chapter 33 : Nonclassical Method of Symmetry Reductions
Chapter 34 : Method of Differential Constraints
Chapter 35 : Painlevé Test for Nonlinear Equations of Mathematical Physics
Chapter 36 : Methods of the Inverse Scattering Problem (Soliton Theory)
Chapter 37 : Conservation Laws
Chapter 38 : Nonlinear Systems of Partial Differential Equations

Part III : Symbolic and Numerical Solutions of Nonlinear PDES with Maple, Mathematical and Matlab
Chapter 39 : Nonlinear Partial Differential Equations with Maple
Chapter 40 : Nonlinear Partial Differential Equations with Mathematica
Chapter 41 : Nonlinear Partial Differential Equations with MATLAB

Part IV : Supplements
Chapter 42 : Painlevé Transcendents
Chapter 43 : Functional Equations

Bibliography
Index

 

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