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Tau Functions and Virasoro Symmetries for Drinfeld-Sokolov Hierarchies

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Tau Functions and the Limit of Block Toeplitz Determinants

A classical way to introduce tau functions for integrable hierarchies of solitonic equations is by means of the Sato–Segal–Wilson infinite-dimensional Grassmannian. Every point in the Grassmannian is…
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On solutions of the two-component Camassa-Holm system

Following the approach of [Chen et al.Lett. Math. Phys. 75, 1–15 (2006)], we continue the study of the two-component Camassa-Holm system by using its relation with the first negative flow of the AKNS…
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On the Drinfeld–Sokolov Hierarchies of D Type

We extend the notion of pseudo-differential operators that are used to represent the Gelfand–Dickey hierarchies and obtain a similar representation for the full Drinfeld–Sokolov hierarchies of D n…
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Borodin–Okounkov formula, string equation and topological solutions of Drinfeld–Sokolov hierarchies

We give a general method to compute the expansion of topological tau functions for Drinfeld–Sokolov hierarchies associated with an arbitrary untwisted affine Kac–Moody algebra. Our method consists of…
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Tau function of the CKP hierarchy and nonlinearizable virasoro symmetries

We introduce a single tau function that represents the C-type Kadomtsev–Petviashvili (CKP) hierarchy in a generalized Hirota ‘bilinear’ equation. The actions on the tau function by additional…
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From additional symmetries to linearization of Virasoro symmetries

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A remark on Kac–Wakimoto hierarchies of D-type

For the Kac–Wakimoto hierarchy constructed from the principal vertex operator realization of the basic representation of the affine Lie algebra D(1)n, we compute the coefficients of the corresponding…
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Drinfeld–Sokolov Hierarchies and Diagram Automorphisms of Affine Kac–Moody Algebras

For a diagram automorphism of an affine Kac–Moody algebra such that the folded diagram is still an affine Dynkin diagram, we show that the associated Drinfeld–Sokolov hierarchy also admits an induced…
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On Properties of Hamiltonian Structures for a Class of Evolutionary PDEs

In a recent paper we proved that for certain class of perturbations of the hyperbolic equation ut = f (u)ux, there exist changes of coordinate, called quasi-Miura transformations, that reduce the…
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