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About this book :-
Handbook of Nonlinear Partial Differential Equations (2E) written by
Andrei D. Polyanin, Valentin F. Zaitsev
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.
This book is helpful for awide audience of researchers, university and college teachers, engineers, and students in various fields of applied mathematics, mechanics, physics, chemistry, biology, economics, and engineering sciences.
(Andrei D. Polyanin, Valentin F. Zaitsev)
Book Detail :-
Title: Handbook of Nonlinear Partial Differential Equations
Edition: 2nd
Author(s): Andrei D. Polyanin, Valentin F. Zaitsev
Publisher: Handbooks of Mathematical Equations
Series: Chapman and Hall/CRC
Year: 2011
Pages: 1878
Type: PDF
Language: English
ISBN: 9781420087246,1420087231,9781420087239
Country: Rassia
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About Author :-
The author Andrei D. Polyanin , D.Se., Ph.D., is a noted scientist of broad interests (ordinary differential, partial differential, and integral equations, mathematical physics, engineering mathematics, nonlinear mechanics, heat and mass transfer. chemical hydrodynamics, and others).
Andrei Polyanin graduated from the Department of Mechanics and Mathematics of the Moscow State University in 1974. He received his Ph.D. degree in 1981 and D.Se. degree in 1986 at the Institute for Problems in Mechanics of the Russian (former USSR) Academy of Sciences. Since 1975, Andrei Polyanin has been a member of the staff of the Institute for Problems in Mechanics of the Russian Academy of Sciences.
Professor Polyanin is an author of 21 books in English. Russian, German, and Bulgarian. His publications also include more than 120 research papers and three patents. In 1991, Andrei Polyanin was awarded a Chaplygin Prize of the USSR Academy of Sciences for his research in mechanics. E-mail: polyanin@ipmncLru
The author Valentin F. Zaitsev , Ph.D., D.Se., is a noted scientist in the fields of ordinary differential equations, mathematical physics, and nonlinear mechanics.
Valentin Zaitsev graduated from the Radio Electronics Faculty of the Leningrad Poly technical Institute (now Saint-Petersburg Technical University) in 1969 and received his Ph.D. degree in 1983 at the Leningrad State University. His Ph.D. thesis was devoted to the group approach to the study of some classes of ordinary differential equations. In 1992, Professor Zaitsev received his Doctor of Sciences degree; his D.Sc. thesis was dedicated to the discrete-group analysis of ordinary differential equations.
In 1971-1996, Valentin Zaitsev worked in the Research Institute for Computational Mathematics and Control Processes of the SL Petersburg State University. Since 1996. Professor Zaitsev has been a member of the staff of the Russian State Pedagogical University.
Professor Zaitsev has made important contributions to new methods in the theory of ordinary and partial differential equations. He is an author of more than 110 scientific publications. including 15 books and one patent. E-mail: z:lltsev@osipenko.stu.neva.ru
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Book Contents :-
Handbook of Nonlinear Partial Differential Equations (2E) written by
Andrei D. Polyanin, Valentin F. Zaitsev
cover the following topics.
Part I. Exact Solutions of Nonlinear Partial Differential Equations
1. First Order Quasilinear Equations
2. First Order Equations with Two Independent Variables Quadratic in Derivatives
3. First Order Nonlinear Equations with Two Independent Variables of General Form
4. First Order Nonlinear Equations with Three orMore Independent Variables
5. Second Order Parabolic Equations with One Space Variable
6. Second Order Parabolic Equations with Two or More Space Variables
7. SecondOrder Hyperbolic Equations with One Space Variable
8. SecondOrder Hyperbolic Equations with Two or More Space Variables
9. SecondOrder Elliptic Equations with Two Space Variables
10. SecondOrder Elliptic Equations with Three or More Space Variables
11. SecondOrder Equations Involving Mixed Derivatives and Some Other Equations
13. ThirdOrder Equations
14. FourthOrder Equations
15. Equations of Higher Orders
16. Systems of Two FirstOrder Partial Differential Equations
17. Systems of Two Parabolic Equations
18. Systems of Two SecondOrder Klein–Gordon Type Hyperbolic Equations
19. Systems of Two Elliptic Equations
20. FirstOrder Hydrodynamic and Other Systems Involving Three or More Equations
21. Navier–Stokes and Related Equations
22. Systems of General Form
Part II. Exact Methods for Nonlinear Partial Differential Equations
23. Methods for Solving FirstOrder Quasilinear Equations
24. Methods for Solving FirstOrder Nonlinear Equations
25. Classification of SecondOrder Nonlinear Equations
26. Transformations of Equations of Mathematical Physics
27. TravelingWave Solutions and SelfSimilar Solutions
28. Elementary Theory of Using Invariants for Solving Equations
29. Method of Generalized Separation of Variables
30. Method of Functional Separation of Variables
31. Direct Method of Symmetry Reductions of Nonlinear Equations
32. Classical Method of Symmetry Reductions
33. Nonclassical Method of Symmetry Reductions
34. Method of Differential Constraints
35. Painlev´e Test for Nonlinear Equations of Mathematical Physics
36. Methods of the Inverse Scattering Problem (Soliton Theory)
37. Conservation Laws
38. Nonlinear Systems of Partial Differential Equations
Part III. Symbolic and Numerical Solutions of Nonlinear PDEs with Maple, Mathematica, and MATLAB
39. Nonlinear Partial Differential Equations with Maple
40. Nonlinear Partial Differential Equations with Mathematica
41. Nonlinear Partial Differential Equations with MATLAB
42. Painlev´e Transcendents
43. Functional Equations
Bibliography
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