KdV hierarchyTau-functionPair of wave functionsMatrix resolventGenerating seriesFor an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic manipulations. Based on this ...
We extend a recent result of [13] for the KdV hierarchy to the Toda lattice hierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we define a pair of wave functions, and use them to give explicit formulae for the generating series of $k$-point correlation functions ...
We study the series expansion of the tau function of the BKP hierarchy applying the addition formulae of the BKP hierarchy. Any formal power series can be expanded in terms of Schur functions. It is known that, under the condition, a formal power seriesis a solution of the KP hierarchy if...
The partition function proves to be a tau function of the Toda lattice hierarchy. The associated linear problem is equivalent to finding the polynomial basis which diagonalizes the partition function. The cases of one Hermitian matrix, one unitary matrix, and Hermitian matrix chains all fall within...
We extend a recent result of [13] for the KdV hierarchy to the Toda lattice\nhierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we\ndefine a pair of wave functions, and use them to give explicit formulae for the\ngenerating series of $k$-point correlation ...
We also study some\nodd-order (($2^n -1$)-order, $ n = 2, 3, ...$) identities which are specific\nfor tau functions, related to the KdV hierarchy.doi:10.1063/1.532873Yordan P. Mishev
We show that V(x,t) is real meromorphic with respect to x\nfor any t>0. We also show that under a very mild additional condition on V_0\nrepresentation implies a strong well-posedness of the KdV equation with such\nV_0's. Among others, our approach yields some relevant results due...
Here we provide a similar description for the Br茅zin-Gross-Witten tau-function. Moreover, we identify both tau-functions of the KdV hierarchy, which describe intersection numbers on the moduli spaces of punctured Riemann surfaces, with the hypergeometric solutions of the BKP hierarchy.Alexan...
Examination of some odd-order identities which are specific for tau functions related to the KdV hierarchy; Problems in translating the identity for the general KdV taus to the cases of the trigonometric functions and elliptic theta functions.Mishev...
Dynamics of general line solitons and breathers on a periodic line waves (PLWs) background in the nonlocal Mel’nikov (MK) equation are investigated via the KP hierarchy reduction method. By constraining different parametric conditions for a general type of tau functions of the KP hierarchy, two...