Results 31 to 40 of about 456 (259)

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

Open Communications in Nonlinear Mathematical Physics
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
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Intertwining operator and integrable hierarchies from topological strings

Journal of High Energy Physics, 2021
In [1], Nakatsu and Takasaki have shown that the melting crystal model behind the topological strings vertex provides a tau-function of the KP hierarchy after an appropriate time deformation.
Jean-Emile Bourgine
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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., Retore, A. L., Spano, N. I., Zimerman, A. H.   +3 more
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A Few Kinds of Loop Algebras and Some Applications

Axioms
In this paper, we search for some approaches for generating (1+1)-dimensional, (2+1)-dimensional and (3+1)-dimensional integrable equations by making use of various Lie algebras and the corresponding loop algebras under the frame of the Tu scheme.
Yanmei Sun, Weiwei Zhang, Nina Xue, Yufeng Zhang   +3 more
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Associativity equations in dispersionless integrable hierarchies

Physics Letters B, 2001
We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda hierarchies. We show, therefore, that any tau-function of dispersionless KP or Toda hierarchy provides a solution to ...
Boyarsky, A.M., Marshakov, A., Ruchayskiy, O., Wiegmann, P., Zabrodin, A.   +4 more
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SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations [PDF]

Open Communications in Nonlinear Mathematical Physics
The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integrable
Y. F. Adans, A. R. Aguirre, J. F. Gomes, G. V. Lobo, A. H. Zimerman   +4 more
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Genus expansion of matrix models and ћ expansion of KP hierarchy

Journal of High Energy Physics, 2020
We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion.
A. Andreev, A. Popolitov, A. Sleptsov, A. Zhabin   +3 more
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An integrable coupling hierarchy of Dirac integrable hierarchy, its Liouville integrability and Darboux transformation

The Journal of Nonlinear Sciences and Applications, 2017
Summary: An integrable coupling hierarchy of Dirac integrable hierarchy is presented by means of zero curvature representation. A Hamiltonian operator involving two parameters is introduced, and it is used to derive a pair of Hamiltonian operators. A bi-Hamiltonian structure of the obtained integrable coupling hierarchy is constructed with the aid of ...
Xu, Xi-Xiang, Sun, Ye-Peng
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Integrating partonomic hierarchies in anatomy ontologies [PDF]

BMC Bioinformatics, 2004
Abstract Background Anatomy ontologies play an increasingly important role in developing integrated bioinformatics applications. One of the primary relationships between anatomical tissues represented in such ontologies is part-of.
Albert Burger, Duncan Davidson, Yiya Yang, Richard A. Baldock   +3 more
openaire   +4 more sources

Solution of tetrahedron equation and cluster algebras

Journal of High Energy Physics, 2021
We notice a remarkable connection between the Bazhanov-Sergeev solution of Zamolodchikov tetrahedron equation and certain well-known cluster algebra expression. The tetrahedron transformation is then identified with a sequence of four mutations.
P. Gavrylenko, M. Semenyakin, Y. Zenkevich   +2 more
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