Results 21 to 30 of about 20,937 (290)
Conformal Maps and Integrable Hierarchies [PDF]
Communications in Mathematical Physics, 2000 Let \(D\) be simply connected domain in the complex \(z\)-plane bounded by a simple analytic curve \(\Gamma\). The authors show that conformal maps \(D\) onto unit disk \(G_1=\{x \mid|z|
Wiegmann, P. B., Zabrodin, A.
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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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Constraints and Soliton Solutions for the KdV Hierarchy and AKNS Hierarchy [PDF]
, 2010 It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a lower-dimensional or fewer ...
C.W. Cao +6 more
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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. +3 more
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dbar-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy [PDF]
, 2001 It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane.
Ahlfors +26 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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Dispersionless (3+1)-dimensional integrable hierarchies [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017 In this 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 integrable hierarchies of (3+1)-dimensional dispersionless systems of the
Maciej Błaszak, Artur Sergyeyev
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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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Analytic-bilinear approach to integrable hierarchies. I. Generalized KP hierarchy [PDF]
Journal of Mathematical Physics, 1998 An analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is proposed. It starts with the generalized Hirota identity for the Cauchy–Baker–Akhiezer (CBA) function and leads to a generalized KP hierarchy in the form of compact functional equations containing a special shift operator.
BOGDANOV L. V., KONOPELCHENKO, Boris
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