55,402 research outputs found
Fay-like identities of the Toda Lattice Hierarchy and its dispersionless limit
In this paper, we derive the Fay-like identities of tau function for the Toda
lattice hierarchy from the bilinear identity. We prove that the Fay-like
identities are equivalent to the hierarchy. We also show that the
dispersionless limit of the Fay-like identities are the dispersionless Hirota
equations of the dispersionless Toda hierarchy.Comment: 20 page
Coupled Modified KP Hierarchy and Its Dispersionless Limit
We define the coupled modified KP hierarchy and its dispersionless limit.
This integrable hierarchy is a generalization of the ''half'' of the Toda
lattice hierarchy as well as an extension of the mKP hierarchy. The solutions
are parametrized by a fibered flag manifold. The dispersionless counterpart
interpolates several versions of dispersionless mKP hierarchy.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
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