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Sato theory on the q-Toda hierarchy and its extension

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  • Li, Chuanzhong

Abstract

In this paper, we construct the Sato theory including the Hirota bilinear equations and tau function of a new q-deformed Toda hierarchy (QTH). Meanwhile the Block type additional symmetry and bi-Hamiltonian structure of this hierarchy are given. From Hamiltonian tau symmetry, we give another definition of tau function of this hierarchy. Afterwards, we extend the q-Toda hierarchy to an extended q-Toda hierarchy (EQTH) which satisfy a generalized Hirota quadratic equation in terms of generalized vertex operators. The Hirota quadratic equation might have further application in Gromov–Witten theory. The corresponding Sato theory including multi-fold Darboux transformations of this extended hierarchy is also constructed. At last, we construct the multicomponent extension of the q-Toda hierarchy and show the integrability including its bi-Hamiltonian structure, tau symmetry and conserved densities.

Suggested Citation

  • Li, Chuanzhong, 2015. "Sato theory on the q-Toda hierarchy and its extension," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 10-23.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:10-23
    DOI: 10.1016/j.chaos.2015.03.008
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