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Nonlinear partial differential equations for scientists and engineers. (English) Zbl 0892.35001
Boston, MA: Birkhäuser. xvii, 593 p. (1997).
This book provides a valuable survey of the many types of nonlinear partial differential equations and their methods of solution that arise throughout science and engineering. The book contains twelve chapters, at the end of each of which are to be found relevant exercises that help build an understanding of the subject matter developed in the chapter, and in many cases provide an extension of material found in the main body of the text.
The width of coverage of material provided by the book can be appreciated from the following listing of chapter headings. 1. Linear partial differential equations; 2. Nonlinear model equations and variational principles; 3. First order quasilinear equations and the method of characteristics; 4. First order nonlinear equations and their applications; 5. Conservation laws and shocks; 6. Kinematic waves and specific real-world nonlinear problems; 7. Nonlinear dispersive waves and Whitham’s equations; 8. Nonlinear diffusion-reaction phenomena, Burgers’ and Fisher’s equations; 9. Solitons and the inverse scattering transform; 10. The nonlinear Schrödinger equation and solitary waves; 11. Nonlinear Klein-Gordon equations; 12. Asymptotic methods and nonlinear evolution equations.
The style of writing is clear and concise and the choice of topics is comprehensive and good, as are the illustrative examples taken from various branches of science and engineering. A bibliography occupying 22 pages located at the end of the book provides a comprehensive and up to date reference source for those who wish to develop their knowledge further, or to refer to various seminal papers that stimulated recent material found in many of the chapters. The author’s strong interest in wave phenomena is reflected by the material found in the last six chapters of the book.
This is a book that can be recommended to graduate students who need a straightforward account of nonlinear partial differential equations that is free from emphasis on the more abstract formulation and methods of solution that are found in many other books.

MSC:
35-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35Q55 NLS equations (nonlinear Schrödinger equations)
35Q51 Soliton equations
35L65 Hyperbolic conservation laws
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