In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.

The first book to approach high oscillation as a subject of its own, Highly Oscillatory Problems begins a new dialogue and lays the groundwork for future research. It ensues from the six-month programme held at the Newton Institute of Mathematical Sciences, which was the first time that different specialists in highly oscillatory research, from diverse areas of mathematics and applications, had been brought together for a single intellectual agenda. This ground-breaking volume consists of eight review papers by leading experts in subject areas of active research, with an emphasis on computation: numerical Hamiltonian problems, highly oscillatory quadrature, rapid approximation of functions, high frequency wave propagation, numerical homogenization, discretization of the wave equation, high frequency scattering and the solution of elliptic boundary value problems.