Frobenius manifolds, integrable hierarchies and minimal Liouville gravity

Abstract: We use the connection between the Frobrenius manifold and the Douglas string equation to further investigate Minimal Liouville gravity. We search a solution of the Douglas string equation and simultaneously a proper transformation from the KdV to the Liouville frame which ensure the fulfilment of the conformal and fusion selection rules. We find that the desired solution of the string equation has explicit and simple form in the flat coordinates on the Frobenious manifold in the general case of (p,q) Minimal Liouville gravity.