# On the moduli space of deformations of bihamiltonian hierarchies of hydrodynamic type

Research paper by Aliaa Barakat

Indexed on: 26 Feb '06Published on: 26 Feb '06Published in: Mathematics - Differential Geometry

#### Abstract

We investigate the deformation theory of the simplest bihamiltonian structure of hydrodynamic type, that of the dispersionless KdV hierarchy. We prove that all of its deformations are quasi-trivial in the sense of B. Dubrovin and Y. Zhang, that is, trivial after allowing transformations where the first partial derivative of the field is inverted. We reformulate the question about deformations as a question about the cohomology of a certain double complex, and calculate the appropriate cohomology group.