Geodesic
A~note on the~extended dispersionless Toda~hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 1, pp. 35-49

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We derive dispersionless Hirota equations for the extended dispersionless Toda hierarchy. We show that the dispersionless Hirota equations are just a direct consequence of the genus-zero topological recurrence relation for the topological $\mathbb CP^1$ model. Using the dispersionless Hirota equations, we compute the two-point functions and express the result in terms of Catalan numbers.
Keywords: extended dispersionless Toda hierarchy, dispersionless Hirota equation, Catalan number, topological field theory. 
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     author = {Niann-Chern Lee and Ming-Hsien Tu},
     title = {A~note on the~extended dispersionless {Toda~hierarchy}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     publisher = {mathdoc},
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     number = {1},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_1_a2/}
}
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Niann-Chern Lee; Ming-Hsien Tu. A~note on the~extended dispersionless Toda~hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 1, pp. 35-49. http://geodesic.mathdoc.fr/item/TMF_2013_175_1_a2/