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
Description
Contents
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.
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