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arXiv · 0808.1444

Loewner equations, Hirota equations and reductions of universal Whitham hierarchy

Kanehisa Takasaki·Takashi Takebe
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Abstract

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 (Löwner-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, Mañas and Mart\'ınez Alonso are reconfirmed in this formulation.

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Kanehisa Takasaki, Takashi Takebe. 2008-09-20. Loewner equations, Hirota equations and reductions of universal Whitham hierarchy. https://doi.org/10.1088/1751-8113/41/47/475206

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