D-bundles and integrable hierarchies

6 D - Bundles and Integrable Hierarchies

Integrable Hierarchies and Wakimoto Modules

In our papers [20, 21] we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy [1] and its generalizations. In particular, we show that the fr...

Hodge Integrals and Integrable Hierarchies

We show that the generating series of some Hodge integrals involving one or two partitions are τ -functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative invariants and integrable hierarchies. The conjecture is verified in some examples.

Topological Strings and Integrable Hierarchies

a Department of Physics, University of Washington at Seattle Seattle, WA 98195-1560, USA b Institute for Theoretical Physics & Korteweg-de Vries Institute for Mathematics University of Amsterdam, 1018 XE Amsterdam, The Netherlands c Physics Department, University of Wisconsin at Madison Madison, WI 53706-1390, USA d Theory Division, CERN, Geneva 23, CH-1211 Switzerland e Jefferson Physical Labo...

Integrable Hierarchies and Wakimoto Realization

In our papers [20, 21] we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV) hierarchies. In this paper we apply our approach to the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy [1] and its generalizations. In particular, we show that the fr...