Abstract
The transition from the zero-genus universal Whitham hierarchy to its dispersionful counterpart, making use only of the Lax representations, is presented. This is an alternative approach to that of Takasaki who has recently shown that the dispersionless limit of the charged multicomponent Kadomtsev-Petviashvili (KP) hierarchy is the Whitham hierarchy. The advantage of the presented approach is the construction of finite-field reductions, which are the main concern in this paper. The theory is illustrated by several significant examples.
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