Handbook of Nonlinear Partial Differential Equations

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