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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
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A Complex Integrable Hierarchy and Its Hamiltonian Structure for Integrable Couplings of WKI Soliton Hierarchy [PDF]
Abstract and Applied Analysis, 2014 We generate complex integrable couplings from zero curvature equations associated with matrix spectral problems in this paper. A direct application to the WKI spectral problem leads to a novel soliton equation hierarchy of integrable coupling system ...
Fajun Yu, Shuo Feng, Yanyu Zhao
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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
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A novel hierarchy of integrable lattices [PDF]
Inverse Problems, 1994 In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector ...
MEROLA, IMMACOLATA +2 more
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Symmetries and integrable systems [PDF]
Fundamental ResearchSymmetry plays key roles in modern physics especially in the study of integrable systems because of the existence of infinitely many local and nonlocal generalized symmetries.
Sen-Yue Lou, Bao-Feng Feng
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Overview of the Kadomtsev–Petviashvili-hierarchy reduction method for solitons
Partial Differential Equations in Applied Mathematics, 2022 The Kadomtsev–Petviashvili (KP) hierarchy reduction method is a prominent direct method for deriving explicit solutions to integrable equations. This method is based on Hirota’s bilinear formulation of integrable systems, as well as the observation that ...
Bo Yang, Jianke Yang
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INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT [PDF]
Reviews in Mathematical Physics, 1995 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 the ordinary KP and Toda hierarchy.
Takasaki, Kanehisa, Takebe, Takashi
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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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Integrable hierarchies and the modular class [PDF]
Annales de l'Institut Fourier, 2008 It is well-known that the Poisson-Nijenhuis manifolds, introduced by Kosmann-Schwarzbach and Magri form the appropriate setting for studying many classical integrable hierarchies. In order to define the hierarchy, one usually specifies in addition to the Poisson-Nijenhuis manifold a bi-hamiltonian vector field.
Damianou, Pantelis A. +1 more
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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
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