UK Nonlinear News, August 1999

A tribute to John Ockendon FRS and John Toland FRS

By John Brindley and Alan Champneys

John Ockendon and John Toland were both elected as members of the Royal Society of London this year. To celebrate their election John Brindley discusses the work of John Ockendon and Alan Champneys discusses the work of John Toland.

The work of John Ockendon FRS

John Brindley

All human beings are unique, but some are more unique than others, and John Ockendon belongs without doubt to that latter subgroup. An Oxford institution for thirty odd years, well remembered by generations of both undergraduate and postgraduate students, he, together with Leslie Fox, as Director of the Computing Laboratory, provided the key support for Alan Tayler in the setting up of the Oxford Study Group for Industry. Subsequently this evolved into the formally constituted OCIAM, of which John was briefly (!) Director following Alan's very sad and premature death. Alan and John made a formidable team; John's incisive and outspoken perceptions, mathematical and otherwise, linking with Alan's more polished diplomatic skills to make innovative and important contributions to the practical solution of a wide range of industrial problems. In many cases these problems motivated highly original and challenging mathematical issues, which led, in the best traditions of applied mathematics, to significant advances in the field of mathematics itself.

Though many other mathematical and numerical practitioners, from Oxford and elsewhere in the UK and overseas, took part in the meetings no one can doubt the prime value of John's input, displaying a wide and deep mathematical knowledge, utilised perceptively and effectively. Of his contributions to many areas of applied maths, perhaps the most important is that to free boundary problems, which occur characteristically in multiphase physical contexts. Through many papers and conference contributions, and even more effectively through challenging (and occasionally provocative) personal interactions, John has inspired great advances in this difficult mathematical area; several former "protégés", now occupying influential University or industrial positions themselves, continue to contribute greatly.

In recent years, John's energies have been employed to great effect in disseminating internationally the best of the Oxford experience in University/industry collaborations. Many Centres and Institutes worldwide now share its commitment to provide industry with valuable advice and support, and at the same time maintain mathematical rigour and stimulate mathematical innovation. For this, as well as for his own wide contributions to applied mathematics, his election to the Royal Society deserves our warm congratulations. i

The work of John Toland FRS

Alan Champneys

In May this year Professor John Toland of the School of Mathematical Sciences, University of Bath was elected a Fellow of the Royal Society. His citation reads a follows:

``Professor Toland is distinguished for his work on non-linear problems in mechanics where he is a master of analytical and topological methods and of their application to physical problems. He has made fundamental contributions to global bifurcation theory and has discovered a new duality principle in the calculus of variations. His studies of waves on water have answered difficult questions that have been open for more than a century.''

John studied as a PhD student at the University of Sussex in the early 1970s under the supervision of Charles Stuart who is now a professor at EPFL Lausanne. He wrote his PhD in 1973 on the topic of Topological Methods for Nonlinear Eigenvalue Problems.

After appointments as a postdoc at the University of Essex in the Fluid Mechanics Research Centre headed by Brooke Benjamin, he went on to become a lecturer at University College London, before being appointed to a chair at Bath in the early 1980s.

John has worked on a range of topics related to Hamiltonian mechanics and variational calculus, and in particular their application to water waves. John's forte is to transform meaningful physical questions into problems in nonlinear functional analysis and to then provide ingenious proofs. In this vein he wrote a series of seminal papers with the late Charles Amick who was a faculty member at University of Chicago until his untimely death in 1991. Among their achievements were existence theories of larger capillary solitary waves and, with J.B. McLeod and L.E. Fraenkel, unraveling the mystery of the approach to the (Stokes) `wave of steepest height'.

His work has also involved the development of novel analytical tools including; with Helmut Hofer a topological method akin to phase plane analysis for 2-degree-of-freedom Hamiltonian systems; with Norman Dancer an application of topological degree to systems which conserve a first integral; and recently with Boris Buffoni and Norman Dancer a new variational approach to sub-harmonic bifurcation of Stokes waves.

In recent years John has continued to bring this deep insight to bear on important physical problems as recognized by his receipt in 1997 of an EPSRC Advanced Fellowship. Recent achievements have included; with Boris Buffoni and Mark Groves a proof of infinite multiplicity of solitary wave solutions to the full Euler-equation formulation of the water wave problem with surface tension; and just this year with P.I. Plotnikov a solution to the long-outstanding (Nash-Moser) problem of the existence of standing water waves.

On a personal level I can say that John is a pleasure to work and talk science with. He is humble to the extent that he will probably hate reading this article for all the `fuss' and embarrassment it will cause (sorry John!). I recall from when I was a mere postdoc working with him how he would go to great lengths not to feel that he was wasting my time, for example by insisting on making photocopies himself rather than letting me do it!

Written with the help of Charlie Stuart and Boris Buffoni who both know John's work better than I do.

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