  To each partition function of cohomological field theory one can associate an
Hamiltonian integrable hierarchy of topological type. The Givental group acts
on such partition functions and consequently on the associated integrable
hierarchies. We consider the Hirota and Lax formulations of the deformation of
the hierarchy of N copies of KdV obtained by an infinitesimal action of the
Givental group. By first deforming the Hirota quadratic equations and then
applying a fundamental lemma to express it in terms of pseudo-differential
operators, we show that such deformed hierarchy admits an explicit Lax
formulation. We then compare the deformed Hamiltonians obtained from the Lax
equations with the analogous formulas obtained in [1, 2], to find that they
agree. We finally comment on the possibility of extending the Hirota and Lax
formulation on the whole orbit of the Givental group action.
