Variational Bihamiltonian Cohomologies and Integrable Hierarchies I: Foundations

Abstract

For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian integrable hierarchy. Moreover, we show that the central invariants of the bihamiltonian structure are preserved under such a linear reciprocal transformation.

Infinite-dimensional Frobenius manifolds underlying an extension of the dispersionless Kadomtsev–Petviashvili hierarchy

“…This important connection between Frobenius manifolds and 2D TFT has led to significant progress in the study of both topics, and has deepened our understanding of the geometric and algebraic structures that arise in these contexts. Please see [4,7,8,9] for details.…”