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Duality of positive and negative integrable hierarchies via relativistically invariant fields
Journal of High Energy Physics, 2021 It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual relations, some ...
Senyue Lou, Lou S Y, Q P Liu
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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 System with Two Integrable Hierarchies [PDF]
Journal of the Physical Society of Japan, 1999 Summary: By assuming the symmetry group and using the inverse method, we find an integrable system which is constructed from superposition of two hierarchies of integrable equations. The authors discuss the SU(2) and SL(2,\(\mathbb{R}\)) cases in detail.
Kakuhata Hiroshi +2 more
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On the Lagrangian Structure of Integrable Hierarchies [PDF]
, 2016 We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler Lagrange equations in their full generality for hierarchies of two-dimensional systems, and construct a pluri-Lagrangian
Yuri Suris +2 more
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Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy [PDF]
Abstract and Applied Analysis, 2014 With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI)
Zhengduo Shan, Hongwei Yang, Baoshu Yin
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Witten’s D 4 integrable hierarchies conjecture [PDF]
Chinese Annals of Mathematics Series B, 2016 We prove that the total descendant potential functions of the theory of Fan-Jarvis-Ruan-Witten for D_4 with symmetry group and D_4^T with symmetry group G_{max}, respectively, are both tau-functions of the D_4 Kac-Wakimoto/Drinfeld-Sokolov hierarchy.
Huijun Fan +2 more
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A multi-component super integrable Dirac hierarchy
Physics Letters B, 2023 We propose a method for generating higher-dimensional nonisospectral super integrable coupling hierarchies associated with a new type of higher-dimensional Lie superalgebra.
Haifeng Wang +2 more
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Using Vector-Product Loop Algebra to Generate Integrable Systems
Axioms, 2023 A new three-dimensional Lie algebra and its loop algebra are proposed by us, whose commutator is a vector product. Based on this, a positive flow and a negative flow are obtained by introducing a new kind of spectral problem expressed by the vector ...
Jian Zhang +3 more
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A new construction of the Drinfeld–Sokolov hierarchies
Partial Differential Equations in Applied Mathematics, 2022 The Drinfeld–Sokolov hierarchies are integrable hierarchies associated with every affine Lie algebra. We present a new construction of such hierarchies, which only requires the computations of a formal Laurent series.
Paolo Casati
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Hamiltonian structures for integrable hierarchies of Lagrangian PDEs [PDF]
Open Communications in Nonlinear Mathematical Physics, 2021 Many integrable hierarchies of differential equations allow a variational description, called a Lagrangian multiform or a pluri-Lagrangian structure. The fundamental object in this theory is not a Lagrange function but a differential $d$-form that is ...
Mats Vermeeren
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