Travelling Waves in Nonlinear Diffusion-Convection Reaction B.H. Gilding and R. Kersner, Birkhauser, Basel (2004), 220 pp., price €88.- ISBN: 3764370718.
Reviewer: Ferdinand Verhulst, University of Utrecht, Netherlands.

Level: intermediate.

Travelling waves are studied in many fields --- physics, chemistry, biology, etc. In this book two aspects are prominently discussed: do travelling waves exist in explicit equations; and, if this is the case, what are the characteristics of the waves? Important examples are considered, among which Fisher's equation, the KPP equation and porous media systems. The basic technique is the formulation of the problem as an integral equation as opposed to the usual phase plane methods. The results are very qualitative but also leading to explicit wave speeds and conditions on the parameters. Occasionally rather exotic examples (as on p. 172) are studied.

What would be the use of this book to readers studying travelling waves? It would be a too technical exercise to use the techniques of this book, but it would make sense to check whether the results of this book provide an existence foundation for more explicit quantitative research.