DrJohn Gibbons

John's interests are in Integrable Hamiltonian systems, particularly those which are dispersionless. Typical of these is the Benney hierarchy, originally derived as a model of long waves on shallow water. This system, with infinitely many dynamical variables, possesses reductions in which only finitely many of these are independent. Such reduced equations can be solved exactly, using the hodograph transformation.

John's research programme is concerned with the classification and the description of such reductions, and the construction of explicit examples of them. Some families of these have been found explicitly in terms of Kleinian sigma functions on algebraic curves. This work has also led to explicit series expansions for such sigma functions, and improved understanding of them.