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We consider the deformations of Whitham systems including the "dispersionterms" and having the form of Dubrovin-Zhang deformations of Frobeniusmanifolds. The procedure is connected with B.A. Dubrovin problem ofdeformations of Frobenius manifolds corresponding to the Whitham systems ofintegrable hierarchies. Under some non-degeneracy requirements we suggest ageneral scheme of the deformation of the hyperbolic Whitham systems using theinitial non-linear system. The general form of the deformed Whitham systemcoincides with the form of the "low-dispersion" asymptotic expansions used byB.A. Dubrovin and Y. Zhang in the theory of deformations of Frobeniusmanifolds.Comment: 27 pages, Late

Whitham systems and deformations