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Hodge Integrals and Integrable Hierarchies [PDF]
Letters in Mathematical Physics, 2010 We show that the generating series of some Hodge integrals involving one or two partitions are tau-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 novel hierarchy of integrable lattices [PDF]
Inverse Problems, 1994 In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector ...
MEROLA, IMMACOLATA +2 more
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Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies
Mathematics, 2023 Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation.
Shou-Ting Chen, Wen-Xiu Ma
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Backlund transformation for integrable hierarchies: example - mKdV hierarchy
Journal of Physics: Conference Series, 2015 Proceedings of the 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent ...
Gomes, J. F. +3 more
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Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy [PDF]
Journal of Mathematical Physics, 1998 An analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is proposed. It starts with the generalized Hirota identity for the Cauchy–Baker–Akhiezer (CBA) function and leads to a generalized KP hierarchy in the form of compact functional equations containing a special shift operator.
BOGDANOV L. V., KONOPELCHENKO, Boris
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A Hierarchy of Integral Operators
Rocky Mountain Journal of Mathematics, 1997 Let \(m\) and \(n\) be integers with \(m+n \geq 0\), \(m^2+ n^2>0\), we define functions \(K_{m,n}\) as follows: \[ K_{m,n} (z)= (-m)! (-1)^m \bigl[(n-1)! \pi\bigr]^{-1} z^{m-1} \overline z^{n-1} \quad \text{for} \quad m\leq 0, \] \[ K_{m,n} (z)= (-n)! (-1)^n\bigl[ (m-1)!
Begehr, Heinrich, Hile, G.N.
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Integrability of generalised type II defects in affine Toda field theory
Journal of High Energy Physics, 2017 The Liouville integrability of the generalised type II defects is investigated. Full integrability is not considered, only the existence of an infinite number of conserved quantities associated with a system containing a defect.
Rebecca Bristow
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Momentum conserving defects in affine Toda field theories
Journal of High Energy Physics, 2017 Type II integrable defects with more than one degree of freedom at the defect are investigated. A condition on the form of the Lagrangian for such defects is found which ensures the existence of a conserved momentum in the presence of the defect.
Rebecca Bristow, Peter Bowcock
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A new kind of anomaly: on W-constraints for GKM
Journal of High Energy Physics, 2021 We look for the origins of the single equation, which is a peculiar combination of W-constrains, which provides the non-abelian W-representation for generalized Kontsevich model (GKM), i.e. is enough to fix the partition function unambiguously. Namely we
A. Morozov
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Defects in the supersymmetric mKdV hierarchy via Bäcklund transformations
Journal of High Energy Physics, 2018 The integrability of the N=1 $$ \mathcal{N}=1 $$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super Bäcklund transformation. The construction of such transformation
A.R. Aguirre +4 more
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