Modulation theory, dispersive shock waves and Gerald Beresford Whitham

Highlights: • Short biography of Gerald Beresford Whitham. • History of Whitham's development of modulation theory. • Importance and applications of modulation theory emphasised. • Development of dispersive shock wave theory outlined. • Relation of modulation theory to Special Issue discussed. Gerald Beresford (GB) Whitham, FRS, (13th December, 1927–26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction–diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham's classic textbook Linear and Nonlinear Waves, published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.