Results 11 to 20 of about 326 (216)
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.
Imai, Koji +2 more
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Topological Strings and Integrable Hierarchies [PDF]
Communications in Mathematical Physics, 2005 We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue
Aganagic, M. +4 more
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Kadomtsev–Petviashvili Hierarchy: Negative Times
Mathematics, 2021 The Kadomtsev–Petviashvili equation is known to be the leading term of a semi-infinite hierarchy of integrable equations with evolutions given by times with positive numbers. Here, we introduce new hierarchy directed to negative numbers of times.
Andrei K. Pogrebkov
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Integrable hierarchies and information measures [PDF]
Journal of Physics A: Mathematical and Theoretical, 2008 11 ...
Parwani, R.R., Pashaev, O.K.
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A generalized isospectral–nonisospectral heat equation hierarchy and its expanding integrable model
Advances in Difference Equations, 2020 A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usual Lax pair into the Lax pairs in Riccati ...
Huanhuan Lu, Yufeng Zhang, Jianqin Mei
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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 ...
S. Y. Lou, X. B. Hu, 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 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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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 Few Integrable Couplings of Some Integrable Systems and (2+1)-Dimensional Integrable Hierarchies
Abstract and Applied Analysis, 2014 Two high-dimensional Lie algebras are presented for which four (1+1)-dimensional expanding integrable couplings of the D-AKNS hierarchy are obtained by using the Tu scheme; one of them is a united integrable coupling model of the D-AKNS hierarchy and the
Binlu Feng, Yufeng Zhang, Huanhe Dong
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