Conformal Maps and Integrable Hierarchies
نویسندگان
چکیده
منابع مشابه
Conformal Maps and Dispersionless Integrable Hierarchies
We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out by the conditions known as ”string equations”. The same hierarchy locally solves the 2D inverse potential problem, i.e., reconstruction of the d...
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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...
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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.
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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...
متن کاملIntegrable 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...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2000
ISSN: 0010-3616
DOI: 10.1007/s002200000249