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- Handbook of Nonlinear Partial Differential Equations

Andrei D. Polyanin, Valentin F. Zaitsev

October 29, 2003
by Chapman and Hall/CRC

Reference
- 840 Pages
- 21 B/W Illustrations

ISBN 9781584883555 - CAT# C3553

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A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity.

Highlights of the Handbook:

PARABOLIC EQUATIONS WITH ONE SPACE VARIABLE

Equations with Power-Law Nonlinearities

Equations with Exponential Nonlinearities

Equations with Hyperbolic Nonlinearities

Equations with Logarithmic Nonlinearities

Equations with Trigonometric Nonlinearities

Equations Involving Arbitrary Functions

Nonlinear Schrödinger Equations and Related Equations

PARABOLIC EQUATIONS WITH TWO OR MORE SPACE VARIABLES

Equations with Two Space Variables Involving Power-Law Nonlinearities

Equations with Two Space Variables Involving Exponential Nonlinearities

Other Equations with Two Space Variables Involving Arbitrary Parameters

Equations Involving Arbitrary Functions

Equations with Three or More Space Variables

Nonlinear Schrödinger Equations

HYPERBOLIC EQUATIONS WITH ONE SPACE VARIABLE

Equations with Power-Law Nonlinearities

Equations with Exponential Nonlinearities

Other Equations Involving Arbitrary Parameters

Equations Involving Arbitrary Functions

Equations of the Form wxy=F(x,y,w, wx, wy )

HYPERBOLIC EQUATIONS WITH TWO OR THREE SPACE VARIABLES

Equations with Two Space Variables Involving Power-Law Nonlinearities

Equations with Two Space Variables Involving Exponential Nonlinearities

Nonlinear Telegraph Equations with Two Space Variables

Equations with Two Space Variables Involving Arbitrary Functions

Equations with Three Space Variables Involving Arbitrary Parameters

Equations with Three Space Variables Involving Arbitrary Functions

ELLIPTIC EQUATIONS WITH TWO SPACE VARIABLES

Equations with Power-Law Nonlinearities

Equations with Exponential Nonlinearities

Equations Involving Other Nonlinearities

Equations Involving Arbitrary Functions

ELLIPTIC EQUATIONS WITH THREE OR MORE SPACE VARIABLES

Equations with Three Space Variables Involving Power-Law Nonlinearities

Equations with Three Space Variables Involving Exponential Nonlinearities

Three-Dimensional Equations Involving Arbitrary Functions

Equations with n Independent Variables

EQUATIONS INVOLVING MIXED DERIVATIVES AND SOME OTHER EQUATIONS

Equations Linear in the Mixed Derivative

Equations Quadratic in the Highest Derivatives

Bellman Type Equations and Related Equations

SECOND-ORDER EQUATIONS OF GENERAL FORM

Equations Involving the First Derivative in t

Equations Involving Two or More Second Derivatives

THIRD-ORDER EQUATIONS

Equations Involving the First Derivative in t

Equations Involving the Second Derivative in t

Hydrodynamic Boundary Layer Equations

Equations of Motion of Ideal Fluid (Euler Equations)

Other Third-Order Nonlinear Equations

FOURTH-ORDER EQUATIONS

Equations Involving the First Derivative in t

Equations Involving the Second Derivative in t

Equations Involving Mixed Derivatives

EQUATIONS OF HIGHER ORDERS

Equations Involving the First Derivative in t and Linear in the Highest Derivative

General Form Equations Involving the First Derivative in t

Equations Involving the Second Derivative in t

Other Equations

SUPPLEMENTS: EXACT METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Classification of Second-Order Semilinear Partial Differential Equations in Two Independent Variables

Transformations of Equations of Mathematical Physics

Traveling-Wave Solutions and Self-Similar Solutions. Similarity Methods

Method of Generalized Separation of Variables

Method of Functional Separation of Variables

Generalized Similarity Reductions of Nonlinear Equations

Group Analysis Methods

Differential Constraints Method

Painlevé Test for Nonlinear Equations of Mathematical Physics

Inverse Scattering Method

Conservation Laws

Hyperbolic Systems of Quasilinear Equations

REFERENCES

INDEX

- E-Streams, Vol 7, No. 10, October 2004

"… exceptionally well organized and clear: the form of the equation is followed by its exact solutions. … It is an easy process to locate the equation of interest. … This handbook follows in the CRC tradition of presenting a complete and usable reference. … A valuable reference work for anyone working with nonlinear partial differential equations. Summing Up: Recommended."

- Choice, June 2004, Vol. 41, No. 10

The authors are to be congratulated for somehow making this book so approachable. From the well-ordered table of contents to the clear index, this book promises to be one that will be used regularly, rather than gather dust on a shelf. Handbook of Nonlinear Partial Differential Equations is a total success from the standpoint of offering a complete, easy-to-use solution guide.

The Industrial Physicist, October/November 2004

Accolades for other "handbooks" by Polyanin and Zaitsev:

- William Schiesser, Lehigh University

"… one-stop shopping for scientists and engineers who need a cookbook solution for partial differential equations. The logical organization--by type of equation…and number of variables--makes finding entries easy. … This very useful book has no competitors."

-CHOICE, on Polyanin's Handbook of Linear Partial Differential Equations for Engineers and Scientists

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