Bihamiltonian Structures of the Genus-Zero Whitham Hierarchy

par Dimitris Makris (IMB)

mardi 19 mai 2026, 16:00 → 17:00 Europe/Paris

318

The genus-zero Whitham hierarchy, introduced in the 1990s by I. M. Krichever, is a family of evolutionary quasi-linear PDEs describing the slow modulation of nonlinear waves. It includes, as special cases, many well-known dispersionless integrable systems, such as the dispersionless KP hierarchy and the two-dimensional Toda hierarchy. In this talk, we explain how to derive a bihamiltonian formulation of the hierarchy using the method of R-matrices. More precisely, we construct a Poisson pencil on the loop space of holomorphic functions defined on disjoint circles in the Riemann sphere, and then apply Dirac reduction to obtain a bihamiltonian structure for the genus-zero Whitham hierarchy. Time permitting, we will also discuss the relationship between this work and the theory of Frobenius manifolds, and propose a conjectural definition of a dispersive deformation of the Whitham hierarchy.