Generalized ILW hierarchy: Solutions and limit to extended lattice GD hierarchy
| Autor: | Kanehisa Takasaki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
High Energy Physics - Theory 14N35 37K10 High Energy Physics - Theory (hep-th) Nonlinear Sciences - Exactly Solvable and Integrable Systems Modeling and Simulation General Physics and Astronomy FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics |
| Popis: | The intermediate long wave (ILW) hierarchy and its generalization, labelled by a positive integer $N$, can be formulated as reductions of the lattice KP hierarchy. The integrability of the lattice KP hierarchy is inherited by these reduced systems. In particular, all solutions can be captured by a factorization problem of difference operators. A special solution among them is obtained from Okounkov and Pandharipande's dressing operators for the equivariant Gromov-Witten theory of $\mathbb{CP}^1$. This indicates a hidden link with the equivariant Toda hierarchy. The generalized ILW hierarchy is also related to the lattice Gelfand-Dickey (GD) hierarchy and its extension by logarithmic flows. The logarithmic flows can be derived from the generalized ILW hierarchy by a scaling limit as a parameter of the system tends to $0$. This explains an origin of the logarithmic flows. A similar scaling limit of the equivariant Toda hierarchy yields the extended 1D/bigraded Toda hierarchy. latex2e using amsmath,amssymb,amsthm, 30 pages, no figure; (v2) sections 2, 3 and 5 are considerably reorganized, accepted for publication |
| Databáze: | OpenAIRE |
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