Handbook of Nonlinear Partial Differential Equations

Handbook of Nonlinear Partial Differential Equations

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Features

  • More specific science and engineering equations and exact solutions than any other book available
  • Many new exact solutions of various nonlinear equations
  • Second-, third-, fourth-, and higher-order equations
  • Special attention to equations of general form that involve arbitrary functions
  • Solutions to equations of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, plasticity theory, nonlinear acoustics, combustion theory, nonlinear optics, theoretical physics, differential geometry, control theory, chemical engineering, and other fields
  • Outlines of basic exact methods for solving nonlinear mathematical physics equations -group analysis methods, direct method for symmetry reductions, differential constraints method, method of generalized separation of variables, and others
  • Many examples illustrating the applications of the methods to specific nonlinear equations and systems of equations
  • An extensive table of contents that provides fast access to the equations of interest
  • Summary

    The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions.

    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:

    Table of Contents

    SOME NOTATIONS AND REMARKS
    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

    Editorial Reviews

    "[T]his book serves as a reference for scientists, mathematicians and engineers. Any research library with strengths in these areas would do well to have this book available, as there are no others quite like it."
    - 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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