Handbook of Nonlinear Partial Differential Equations

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