Results 11 to 20 of about 8,648 (287)

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 ...
S. Y. Lou, X. B. Hu, Q. P. Liu
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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
doaj   +1 more source

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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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.
Fan, Huijun, Francis, Amanda, Jarvis, Tyler, Merrell, Evan, Ruan, Yongbin   +4 more
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Generating of Nonisospectral Integrable Hierarchies via the Lie-Algebraic Recursion Scheme

Mathematics, 2020
In the paper, we introduce an efficient method for generating non-isospectral integrable hierarchies, which can be used to derive a great many non-isospectral integrable hierarchies.
Haifeng Wang, Yufeng Zhang
doaj   +1 more source

Deformation conjecture: deforming lower dimensional integrable systems to higher dimensional ones by using conservation laws

Journal of High Energy Physics, 2023
Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm.
S. Y. Lou, Xia-zhi Hao, Man Jia
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Generating nonisospectral integrable hierarchies via a new scheme

Advances in Difference Equations, 2020
In the paper, an efficient and straightforward method for generating nonisospectral integrable hierarchies is introduced. It follows that we consider the application related to Lie algebra gl ( 3 ) $\operatorname{gl}(3)$ based on the method.
Haifeng Wang, Yufeng Zhang
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Integrable coupled massive Thirring model with field values in a Grassmann algebra

Journal of High Energy Physics, 2023
A coupled massive Thirring model of two interacting Dirac spinors in 1 + 1 dimensions with fields taking values in a Grassmann algebra is introduced, which is closely related to a SU(1) version of the Grassmannian Thirring model also introduced in this ...
B. Basu-Mallick, F. Finkel, A. González-López, D. Sinha   +3 more
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Integrable Hamiltonian Hierarchies [PDF]

, 2008
Preface In the past decades now a famous class of evolution equations has been discovered and intensively studied, a class including the nowadays celebrated Korteweg-de Vries equation, sine-Gordon equation, nonlinear Schr ̈odinger equation, etc. The equations from this class are known also as the soliton equations or equations solvable by the so ...
GERDJIKOV, VLADIMIR, VILASI, Gaetano, YANOVSKI A. B.   +2 more
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Liouville Correspondences between Integrable Hierarchies [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2017
In this paper, we study explicit correspondences between the integrable Novikov and Sawada-Kotera hierarchies, and between the Degasperis-Procesi and Kaup-Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada-Kotera equations, and the isospectral problems of the Degasperis ...
Kang, J., Liu, X., Olver, P.J., Qu, C.
openaire   +4 more sources