1 research outputs found
Loewner equations, Hirota equations and reductions of universal Whitham hierarchy
This paper reconsiders finite variable reductions of the universal Whitham
hierarchy of genus zero in the perspective of dispersionless Hirota equations.
In the case of one-variable reduction, dispersionless Hirota equations turn out
to be a powerful tool for understanding the mechanism of reduction. All
relevant equations describing the reduction (L\"owner-type equations and
diagonal hydrodynamic equations) can be thereby derived and justified in a
unified manner. The case of multi-variable reductions is not so
straightforward. Nevertheless, the reduction procedure can be formulated in a
general form, and justified with the aid of dispersionless Hirota equations. As
an application, previous results of Guil, Ma\~{n}as and Mart\'{\i}nez Alonso
are reconfirmed in this formulation.Comment: latex 2e using packages amsmath,amssymb,amsthm, 39 pages, no figure;
(v2) a few typos corrected and accepted for publicatio