The notion of non-degenerate solutions for the dispersionless Toda hierarchy<br />
is generalized to the universal Whitham hierarchy of genus zero with $M+1$<br />
marked points. These solutions are characterized by a Riemann-Hilbert problem<br />
(generalized string equations) with respect to two-dimensional canonical<br />
transformations, and may be thought of as a kind of general solutions of the<br />
hierarchy. The Riemann-Hilbert problem contains $M$ arbitrary functions<br />
$H_a(z_0,z_a)$, $a = 1,...,M$, which play the role of generating functions of<br />
two-dimensional canonical transformations. The solution of the Riem...