Bernard Deconinck's Research
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A solution to the KP equation
- Role
- The Kadomtsev-Petviashvili equation
- Project Collaborators
- Bernard Deconinck
- Mark van Hoeij
- Matt Patterson
- Harvey Segur
- Project Description
One research topic is the study of finite-genus solutions of the Kadomtsev-Petviashvili (KP) equation. The KP equation
describes the evolution of long, almost one-dimensional waves in shallow water.
The equation has a large class of quasi-periodic solutions which are
parametrized by compact, connected Riemann surfaces of arbitrary genus. This
parametrization is very transcendental. Making these solutions effective, to the
point where they can be compared to experiments, is one of the focal points of
my research. This is a long-term project which has led to the construction of
Maple programs for black-box computation with Riemann
surfaces.