Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol