Nonlinear wave processes in acoustics.

*(English)*Zbl 0908.76003
Cambridge Texts in Applied Mathematics. 9. Cambridge: Cambridge University Press. x, 298 p. (1998).

This is a very good book about a theoretical subject that has at times appeared to have enormous practical significance. Much of that significance lay in defence, so much of the very large theoretical effort that has been applied to the subject over the last 50 years was not available in the open literature. Soviet work, which frequently appeared (rightly or wrongly) to be more effective than that of the West, has always fascinated Western acousticians – and it is this work which forms the bulk of this book, very clearly written and set alongside Western models by two masters of the subject. The translation from Russian to English shows little of the stylistic difficulties that commonly spoil translated scientific texts.

The emphasis of the book is on the effects of nonlinearity, theoretically more difficult to handle and therefore necessarily much more restricted in scope than are the linear processes of acoustics. But nonlinear effects provide their own fascination; to the applied mathematicians, a justification and relevance for their powerful new techniques of analysis, and for the acoustician anomalous effects that couple otherwise independent fields and upset the energy balance. As the authors point out in the preface, there is a tendency for the most understood nonlinear processes to be confined to the very nearly linear waves that owe most of their character to linear fields that are understood very well. But useful waves are often better if they are stronger, giving cases where usually small effects are big enough to dominate a particular interest and importance. Many of these are clearly described in this book together with their individual characteristic equations and their methods of analysis. One cannot but admire the wide scope of the subject, the breadth of the book’s coverage, and the skill of its authors. One knows though that by being restricted to depart only gently from simple waves, the book is relevant to only a very small subset of the waves occurring in the natural world.

The emphasis of the book is on the effects of nonlinearity, theoretically more difficult to handle and therefore necessarily much more restricted in scope than are the linear processes of acoustics. But nonlinear effects provide their own fascination; to the applied mathematicians, a justification and relevance for their powerful new techniques of analysis, and for the acoustician anomalous effects that couple otherwise independent fields and upset the energy balance. As the authors point out in the preface, there is a tendency for the most understood nonlinear processes to be confined to the very nearly linear waves that owe most of their character to linear fields that are understood very well. But useful waves are often better if they are stronger, giving cases where usually small effects are big enough to dominate a particular interest and importance. Many of these are clearly described in this book together with their individual characteristic equations and their methods of analysis. One cannot but admire the wide scope of the subject, the breadth of the book’s coverage, and the skill of its authors. One knows though that by being restricted to depart only gently from simple waves, the book is relevant to only a very small subset of the waves occurring in the natural world.

Reviewer: J.E.Ffowcs Williams (Cambridge)