Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-08-11
J. Phys. A: Math. Theor. 41 (2008), 475206 (27pp)
Nonlinear Sciences
Exactly Solvable and Integrable Systems
latex 2e using packages amsmath,amssymb,amsthm, 39 pages, no figure; (v2) a few typos corrected and accepted for publication
Scientific paper
10.1088/1751-8113/41/47/475206
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.
Takasaki Kanehisa
Takebe Takashi
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