  We study solutions to the Kadomtsev-Petviashvili equation whose underlying
algebraic curves undergo tropical degenerations. Riemann's theta function
becomes a finite exponential sum that is supported on a Delaunay polytope. We
introduce the Hirota variety which parametrizes all tau functions arising from
such a sum. We compute tau functions from points on the Sato Grassmannian that
represent Riemann-Roch spaces and we present an algorithm that finds a soliton
solution from a rational nodal curve.
