Transformations of integrable hydrodynamic chains and their hydrodynamic reductions

Hydrodynamic reductions of the hydrodynamic chain associated with the dispersionless limit of the 2+1-dimensional Harry-Dym equation are found by using the Miura type and reciprocal transformations applied to the Benney hydrodynamic chain. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 167–175, 2006.