The Naylor Prize for 2000 is awarded to Professor A.S. Fokas of Imperial College, London. He has made substantial contributions to the theory of integrable systems and to the theory of other important linear and nonlinear equations, including boundary-value problems. He has established himself as a leading analyst worldwide in these significant areas of applied mathematics.

One main theme of Thanasis Fokas’ work has been that of integrable systems of partial differential equations, and the role of inverse scattering and other methods for solving such equations. With collaborators, he was in the vanguard with the introduction of the concepts of master symmetry and of bi-Hamiltonian structures, and in the development of the Riemann-Hilbert and so-called d-bar methods for solving partial differential equations in, for example, two space dimensions and one time dimension, such as the Kadomtsev-Petviashvili (KP) equation.

In further joint work, Fokas showed how the famous inverse scattering approach could be exploited to solve other linear and nonlinear problems with nontrivial boundary and initial conditions. In this regard the formulation in terms of Lax pairs proved to be invaluable, especially the realisation by Fokas that the two Lax equations, when analysed simultaneously and when supplemented with the analysis of a global relation, enabled solutions to be obtained by the Riemann-Hilbert or d-bar methods. This pioneering work is expected to have major ramifications for elucidating the behaviour of partial differential equations.

Professor Fokas is playing a unique and pivotal role in the developments, which are outlined above, both in this country and worldwide.

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