A. Polyanin – Handbook of Nonlinear Partial Differential Equations (2nd edition)

Автор: A. Polyanin
Название книги: Handbook of Nonlinear Partial Differential Equations (2nd edition)
Формат: PDF
Жанр: Математика
Страницы: 1878
Качество: Изначально компьютерное, E-book

The Handbook of Nonlinear Partial Differential Equations, a unique reference for
scientists and engineers, contains over 3,000 nonlinear partial differential equations with
solutions, as well as exact, symbolic, and numerical methods for solving nonlinear equations.
First,
second,
third,
fourth,
and higherorder
nonlinear equations and systems of
equations are considered. Equations of parabolic, hyperbolic, elliptic, mixed, and general
types are discussed. A large number of new exact solutions to nonlinear equations are
described. In total, the handbook contains several times more nonlinear PDEs and exact
solutions than any other book currently available.
In selecting the material, the authors gave the highest priority to the following fivemajor
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 forwhich 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 partial differential equations or
linear integral equations.
The second edition 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 second edition:
• Firstorder
nonlinear partial differential equations with solutions.
• Some second,
third,
fourth,
and higherorder
nonlinear equations with solutions.
• Parabolic, hyperbolic, elliptic, and other systems of equations with solutions.
• Some exact methods and transformations.
• Symbolic and numerical methods for solving nonlinear PDEswithMaple,Mathematica,
and MATLAB.
• Many new examples and tables included for illustrative purposes.
• A large list of references consisting of over 1,300 sources.
• Extensive table of contents and detailed index.
Note that the first part of the book can be used as a database of test problems for
numerical and approximate methods for solving nonlinear partial differential equations.
We would like to express our deep gratitude to Alexei Zhurov and Alexander Aksenov
for fruitful discussions and valuable remarks. We are very thankful to Inna Shingareva and
Carlos Liz´arragaCelaya
who wrote three chapters (39–41) of the book at our request