The lift on a small sphere in a slow shear flow - Corrigendum

Abstract

Also, the diagram with its handwritten equations shows at its worst the disadvantages of a photocopied typescript. The first chapter is a very readable account of the history and mathematical properties of the Korteweg-de Vries equation. I was particularly impressed with the nice motivation for the Miura transform to the linear Schrodinger equation. The second chapter comes as a bit of a jolt. The reader is thrown right into the inversescattering transform with ( a considerable amount of hard explicit computations and estimates’. The third chapter with its neat analysis and punning sub-title The Lax Approach comes as light relief. However, with chapter 4 it is back to the scattering problem. After this the generalizations to matrix systems and to nonuniformities in the remaining thiee chapters are comparatively straightforward. A perennial blessing throughout the book is that, although a great deal of concentration is given to make each step totally secure, there are regular reminders and explanations of the overall plan. This is certainly not a book to be dipped into or skimmed. There is a lot of notation to be absorbed in order to follow the arguments, and many details are left to the reader. However, for any mathematician interested in solitons the effort of working through Eckhaus & van Harten’s book is well worth it. RONALD SMITH