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

Towards Lax formulation of integrable hierarchies of topological type