John Gibbons
(Imperial College, UK)

Hyperelliptic and cyclic trigonal reductions of the Benney hierarchy

The reductions of the Benney hierarchy to a system with N Riemann invariants can be described by an N-parameter family of conformal maps to domains with N slits, parametrised by the variable endpoints of the slits - these are the Riemann invariants. Some such reductions can be constructed as Schwartz-Christoffel mappings - two such families are described, and examples constructed explicitly in terms of Kleinian sigma functions.