Abstract
In the first part of this paper we consider the transformation of the cubic identities for general Korteweg–de Vries (KdV) tau functions from [Mishev, J. Math. Phys. 40, 2419–2428 (1999)] to the specific identities for trigonometric KdV tau functions. Afterwards, we consider the Fay identity as a functional equation and provide a wide set of solutions of this equation. The main result of this paper is Theorem 3.4, where we generalize the identities from Mishev. An open problem is the transformation of the cubic identities from Mishev to the specific identities for elliptic KdV tau functions.
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