Linear and nonlinear waves. Paperback ed. (English) Zbl 0940.76002

Whitham, Gerald B.

Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs, and Tracts. New York, NY: Wiley. xvi, 636 p. (1999).

The re-issue of this excellent book on linear and nonlinear waves in paperback form is to be welcomed. When it first appeared in 1974 [G. B. Whitham, Linear and nonlinear waves. Pure and Applied Mathematics, A Wiley-Interscience Series of Texts, Monographs and Tracts. New York etc.: John Wiley & Sons. XVI (1994; Zbl 0373.76001)], it was the first book to present a comprehensive account of the many types of waves that occur both with and without dispersion. It surveyed the general subject of waves in a clear manner with many applications described in some detail, and these accounts are as relevant now as they were when the book first appeared.
It provides an admirable introduction to the general study of waves, and it is sufficiently detailed to be of direct use in all but the most complicated wave propagation problems. The subject has advanced in many areas since 1974, particularly in the areas of shock waves and solitons, but the introduction provided in the book is still as valuable as ever for research students entering this general area.
No changes have been made to the first edition, and the only thing to be regretted is the rather high price charged for this paperback reprint.

Reviewer: A.Jeffrey (Newcastle upon Tyne)

MSC:

76-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to fluid mechanics
74-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mechanics of deformable solids
35-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations
76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25	Solitary waves for incompressible inviscid fluids
76L05	Shock waves and blast waves in fluid mechanics
74Jxx	Waves in solid mechanics

Keywords:

hyperbolic waves; diffusive waves; shocks; water waves; solitons

Citations:

Zbl 0373.76001