Topological analysis corresponding to the Borisov–Mamaev–Sokolov integrable system on the Lie algebra so(4)

2016 ◽  
Vol 21 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Rasoul Akbarzadeh
Keyword(s):  
Lie Algebra ◽  
Integrable System ◽  
Topological Analysis

Soliton Connection of the sinh-Gordon Equation

1984 ◽  
Vol 39 (9) ◽  
pp. 917-918 ◽  
Author(s):  
A. Grauel
Keyword(s):  
Differential Equations ◽  
Lie Algebra ◽  
Integrable System ◽  
Gordon Equation ◽  
Nonlinear Differential Equations ◽  
Differential Forms ◽  
Completely Integrable ◽  
Completely Integrable System ◽  
Derivatives Of

It is demonstrated that the sinh-Gordon equation can be written as covariant exterior derivatives of Lie algebra valued differential forms and, moreover, that these nonlinear differential equations represent a completely integrable system.

scholarly journals An extension of Lie algebra and a related integrable system

2004 ◽  
Vol 53 (5) ◽  
pp. 1276
Author(s):  
Zhang Yu-Feng ◽  
Guo Fu-Kui
Keyword(s):  
Lie Algebra ◽  
Integrable System

scholarly journals ON A CLASS OF INTEGRABLE SYSTEMS CONNECTED WITH GL(N,ℝ)

2004 ◽  
Vol 19 (supp02) ◽  
pp. 205-216 ◽  
Author(s):  
A. GERASIMOV ◽  
S. KHARCHEV ◽  
D. LEBEDEV
Keyword(s):  
Lie Algebra ◽  
Integrable System ◽  
Integrable Systems ◽  
Cotangent Bundle ◽  
Spectral Curve ◽  
The Other ◽  
Quantum Integrable Systems ◽  
New Class ◽  
Integrable Theory

In this paper we define a new class of the quantum integrable systems associated with the quantization of the cotangent bundle T*(GL(N)) to the Lie algebra [Formula: see text]. The construction is based on the Gelfand-Zetlin maximal commuting subalgebra in [Formula: see text]. We discuss the connection with the other known integrable systems based on T*GL(N). The construction of the spectral tower associated with the proposed integrable theory is given. This spectral tower appears as a generalization of the standard spectral curve for an integrable system.

scholarly journals Nonlocal PT-Symmetric Integrable Equations of Fourth-Order Associated with so(3, ℝ)

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2130
Author(s):  
Li-Qin Zhang ◽  
Wen-Xiu Ma
Keyword(s):  
Conservation Laws ◽  
Lie Algebra ◽  
Integrable System ◽  
Fourth Order ◽  
Reverse Time ◽  
Integrable Equations

The paper aims to construct nonlocal PT-symmetric integrable equations of fourth-order, from nonlocal integrable reductions of a fourth-order integrable system associated with the Lie algebra so(3,R). The nonlocalities involved are reverse-space, reverse-time, and reverse-spacetime. All of the resulting nonlocal integrable equations possess infinitely many symmetries and conservation laws.

scholarly journals (2+1)-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Chunlei Wang ◽  
Yong Zhang ◽  
Baoshu Yin ◽  
Xiaoen Zhang
Keyword(s):  
Solitary Wave ◽  
Riccati Equation ◽  
Lie Algebra ◽  
Integrable System ◽  
Solitary Waves ◽  
Mkdv Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Rossby Solitary Waves ◽  
Mkdv Hierarchy

By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new (2+1)-dimensional mKdV hierarchy is derived which popularizes the results of (1+1)-dimensional integrable system. Furthermore, the (2+1)-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the (1+1)-dimensional mKdV equation. By virtue of Riccati equation, some solutions of (2+1)-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.

scholarly journals AN EQUIVARIANT DESCRIPTION OF CERTAIN HOLOMORPHIC SYMPLECTIC VARIETIES

2018 ◽  
Vol 97 (2) ◽  
pp. 207-214 ◽  
Author(s):  
PETER CROOKS
Keyword(s):  
Lie Algebra ◽  
Integrable System ◽  
Integrable Systems ◽  
Semisimple Group ◽  
Theoretical Physics ◽  
Hyperkähler Manifolds ◽  
Complex Semisimple ◽  
Hyperkähler Geometry ◽  
Symplectic Varieties

Varieties of the form$G\times S_{\!\text{reg}}$, where$G$is a complex semisimple group and$S_{\!\text{reg}}$is a regular Slodowy slice in the Lie algebra of$G$, arise naturally in hyperkähler geometry, theoretical physics and the theory of abstract integrable systems. Crooks and Rayan [‘Abstract integrable systems on hyperkähler manifolds arising from Slodowy slices’,Math. Res. Let., to appear] use a Hamiltonian$G$-action to endow$G\times S_{\!\text{reg}}$with a canonical abstract integrable system. To understand examples of abstract integrable systems arising from Hamiltonian$G$-actions, we consider a holomorphic symplectic variety$X$carrying an abstract integrable system induced by a Hamiltonian$G$-action. Under certain hypotheses, we show that there must exist a$G$-equivariant variety isomorphism$X\cong G\times S_{\!\text{reg}}$.

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