Results 1 to 10 of about 8,531 (172)
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 +6 more sources
Integrable Hierarchies and Dispersionless Limit [PDF]
Reviews in Mathematical Physics, 1994 Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of
Takasaki, Kanehisa, Takebe, Takashi
core +3 more sources
Manifestly Supersymmetric Lax Integrable Hierarchies [PDF]
Physics Letters B, 1996 A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained.
Aratyn, H., Rasinariu, C.
core +4 more sources
Topological Strings and Integrable Hierarchies [PDF]
Communications in Mathematical Physics, 2003 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.
Aganagic +42 more
core +5 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 +5 more sources
Integrable Hierarchies and Information Measures [PDF]
Journal of Physics A: Mathematical and Theoretical, 2007 In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimesional isentropic fluid, with an appropriately motivated ...
Ablowitz M +13 more
core +3 more sources
Nonlinear Integrable Couplings of Levi Hierarchy and WKI Hierarchy [PDF]
Abstract and Applied Analysis, 2014 With the help of the known Lie algebra, a type of new 8-dimensional matrix Lie algebra is constructed in the paper. By using the 8-dimensional matrix Lie algebra, the nonlinear integrable couplings of the Levi hierarchy and the Wadati-Konno-Ichikawa (WKI)
Zhengduo Shan, Hongwei Yang, Baoshu Yin
doaj +4 more sources
On the compatible weakly nonlocal Poisson brackets of hydrodynamic type [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 We consider the pairs of general weakly nonlocal Poisson brackets of hydrodynamic type (Ferapontov brackets) and the corresponding integrable hierarchies.
Andrei Ya. Maltsev
doaj +4 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 +2 more
doaj +1 more source
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
doaj +1 more source