Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-02-25
J.Phys.A43:434032,2010
Nonlinear Sciences
Exactly Solvable and Integrable Systems
latex2e, usepackage amsmath,amssymb, 19 pages, no figure; (v2) typos corrected, final version for publication
Scientific paper
10.1088/1751-8113/43/43/434032
The extended Toda hierarchy of Carlet, Dubrovin and Zhang is reconsidered in the light of a 2+1D extension of the 1D Toda hierarchy constructed by Ogawa. These two extensions of the 1D Toda hierarchy turn out to have a very similar structure, and the former may be thought of as a kind of dimensional reduction of the latter. In particular, this explains an origin of the mysterious structure of the bilinear formalism proposed by Milanov.
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