Handbook of Nonlinear Partial Differential Equations: Second Edition

In selecting the material, the authors gave the highest priority to the following five major types of equations:

• Equations that arise in various applications (heat and mass transfer theory, wave theory, nonlinear mechanics, hydrodynamics, gas dynamics, plasticity theory, nonlinear acoustics, combustion theory, nonlinear optics, theoretical physics, differential geometry, control theory, chemical engineering sciences, biology, and others).

• Equations of general form that depend on arbitrary functions; exact solutions of such equations are of principal value for testing numerical and approximate methods.

• Equations for which the general solution or solutions of quite general form, with arbitrary functions, could be obtained.

• Equations that involve many free parameters.

• Equations whose solutions are reduced to solving linear PDEs or linear integral equations.

The 2e has been substantially updated, revised, and expanded. More than 1,500 new equations with exact solutions, as well some methods and many examples, have been added. The new edition has been increased by a total of over 1,000 pages.

New to the 2e:

• 1st order nonlinear PDEs with solutions.

• Some 2nd, 3rd, 4th, and higher order nonlinear equations with solutions.

• Parabolic, hyperbolic, elliptic, and other systems of equations with solutions.

• Some exact methods and transformations. …