Results 1 to 10 of about 4,761,670 (353)

Dispersionless (3+1)-dimensional integrable hierarchies. [PDF]

Proc Math Phys Eng Sci, 2017
In the present paper we introduce a multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies. Applying this method to the case of the Lie algebra of functions with respect to the contact bracket, we construct ...
Błaszak M, Sergyeyev A.
europepmc   +8 more sources

Duality of positive and negative integrable hierarchies via relativistically invariant fields [PDF]

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
doaj   +2 more sources

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, Yufeng Zhang, Chuanzhong Li   +2 more
doaj   +2 more sources

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
doaj   +3 more sources

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   +2 more sources

Flat F-Manifolds, F-CohFTs, and Integrable Hierarchies [PDF]

Communications in Mathematical Physics, 2021
We define the double ramification hierarchy associated to an F-cohomological field theory and use this construction to prove that the principal hierarchy of any semisimple (homogeneous) flat F-manifold possesses a (homogeneous) integrable dispersive ...
Alessandro Arsie, Alexandr Buryak, Paolo Lorenzoni, Paolo Rossi   +3 more
openalex   +3 more sources

Integrable discretization of recursion operators and unified bilinear forms to soliton hierarchies [PDF]

Open Communications in Nonlinear Mathematical Physics, 2017
In this paper, we give a procedure for discretizing recursion operators by utilizing unified bilinear forms within integrable hierarchies. To illustrate this approach, we present unified bilinear forms for both the AKNS hierarchy and the KdV hierarchy ...
Xingbiao Hu, Guofu Yu, Yingnan Zhang
doaj   +4 more sources

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
doaj   +2 more sources

Matrix mKdV Integrable Hierarchies via Two Identical Group Reductions

Mathematics
This paper applies a pair of identical group reductions or similarity transformations to formulate integrable models. An application to the Ablowitz–Kaup–Newell–Segur (AKNS) matrix spectral problems leads to reduced matrix modified Korteweg–de Vries ...
Wen-Xiu Ma
doaj   +2 more sources

Hopf link invariants and integrable hierarchies

Physics Letters B
The goal of this note is to study integrable properties of a generating function of the HOMFLY-PT invariants of the Hopf link colored with different representations.
Chuanzhong Li, A. Mironov, A.Yu. Orlov
doaj   +2 more sources