New completely integrable cases of two- or three-dimensional systems of the Toda lattice type

2000 ◽  
Vol 270 (1-2) ◽  
pp. 62-74
Author(s):  
Puyun Gao
Keyword(s):  
Toda Lattice ◽  
Three Dimensional ◽  
Completely Integrable ◽  
Lattice Type

Lattice-Type Polymers from an Adduct of C60 and 2-Methylaziridine

1994 ◽  
Vol 359 ◽  
Author(s):  
A. Nigam ◽  
T. Shekharam ◽  
T. N. Bharadwaj ◽  
J. Giovanola ◽  
S. C. Narang ◽  
...  
Keyword(s):  
Bisphenol A ◽  
Three Dimensional ◽  
Solid Lubricants ◽  
Wear Properties ◽  
Lattice Type ◽  
Potential Use

ABSTRACTA one to ten adduct of C60 and 2-methylaziridine was prepared and copolymerized with Novolac, Epon and Bisphenol A to obtain three dimensional polymers containing C60 with low coefficients of friction and good wear properties, which bode well for their potential use as solid lubricants.

An L–A pair for the Hess–Apel'rot system and a new integrable case for the Euler–Poisson equations on so(4) × so(4)

2001 ◽  
Vol 131 (4) ◽  
pp. 845-855 ◽  
Author(s):  
Vladimir Dragović ◽  
Borislav Gajić
Keyword(s):  
Three Dimensional ◽  
Classification Theorem ◽  
Geometric Integration ◽  
Integrable Case ◽  
Integration Procedure ◽  
Completely Integrable ◽  
Poisson Equations ◽  
Corrected Version ◽  
Explicit Formulae

We present an L–A pair for the Hess–Apel'rot case of a heavy rigid three-dimensional body. Using it, we give an algebro-geometric integration procedure. Generalizing this L–A pair, we obtain a new completely integrable case of the Euler–Poisson equations in dimension four. Explicit formulae for integrals that are in involution are given. This system is a counterexample to one of Ratiu's theorems. A corrected version of this classification theorem is proved.

scholarly journals GEOMETRIZATION OF THE LAX PAIR TENSORS

2000 ◽  
Vol 15 (24) ◽  
pp. 1503-1510 ◽  
Author(s):  
D. BALEANU ◽  
S. BAŞKAL
Keyword(s):  
Toda Lattice ◽  
Dimensional Space ◽  
Torsion Tensor ◽  
Three Dimensional ◽  
Lax Pair ◽  
Three Dimensional Space

The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional space–times admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.

scholarly journals On the complete integrability of the periodic quantum Toda lattice

2017 ◽  
Vol 29 (6) ◽  
Author(s):  
Augustin-Liviu Mare
Keyword(s):  
Dynkin Diagram ◽  
Toda Lattice ◽  
Complete Integrability ◽  
Completely Integrable ◽  
Quantum Toda Lattice ◽  
Extended Dynkin Diagram

AbstractWe prove that the periodic quantum Toda lattice corresponding to any extended Dynkin diagram is completely integrable. This has been conjectured and proved in all classical cases and

Decomposing the Toda hierarchy by an implicit symmetry constraint

2019 ◽  
Vol 33 (03) ◽  
pp. 1950028
Author(s):  
Xi-Xiang Xu ◽  
Min Guo ◽  
Ning Zhang
Keyword(s):  
Hamiltonian System ◽  
Toda Lattice ◽  
Lattice Equation ◽  
Symmetry Constraint ◽  
Completely Integrable ◽  
Toda Hierarchy ◽  
Finite Dimensional ◽  
Symplectic Map ◽  
Toda Lattice Hierarchy

An implicit symmetry constraint of the famous Toda lattice hierarchy is presented. Using this symmetry constraint, every lattice equation in the Toda hierarchy is decomposed by an integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system.

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