Generalized Dicke model as an integrable dynamical system inverse to the nonlinear Schr�dinger equation

1995 ◽  
Vol 47 (1) ◽  
pp. 149-151 ◽  
Author(s):  
R. V. Samulyak
Keyword(s):  
Dynamical System ◽  
Integrable Dynamical System ◽  
Dinger Equation ◽  
Dicke Model

Vector Product and an Integrable Dynamical System

2011 ◽  
Vol 56 (6) ◽  
pp. 992-994
Author(s):  
Willi-Hans Steeb ◽  
Yorick Hardy ◽  
Igor Tanski
Keyword(s):  
Dynamical System ◽  
Vector Product ◽  
Integrable Dynamical System

scholarly journals Degenerate Dynamical Systems and the Disappearance of (K.A.M.-Type) Integrals of Motion

1983 ◽  
Vol 74 ◽  
pp. 411-415
Author(s):  
H. Varvoglis
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Integrals Of Motion ◽  
Integrable Dynamical System

ABSTRACTThe problem of constructing the stochasticity criterion of a degenerate near-integrable dynamical system is considered. We show that in certain cases the above criterion can be found as the limit of the corresponding stochasticity criteria of a family of non-degenerate systems, whose limit is the degenerate one.

scholarly journals Fusion Rules for Quantum Transfer Matrices as a Dynamical System on Grassmann Manifolds

1997 ◽  
Vol 12 (19) ◽  
pp. 1369-1378 ◽  
Author(s):  
O. Lipan ◽  
P. B. Wiegmann ◽  
A. Zabrodin
Keyword(s):  
Dynamical System ◽  
Quantum Model ◽  
Young Diagrams ◽  
Transfer Matrices ◽  
Integrable Dynamical System ◽  
Hirota Equation ◽  
Functional Relations ◽  
Bilinear Functional ◽  
Bilinear Relations ◽  
Integrable Quantum Model

We show that the set of transfer matrices of an arbitrary fusion type for an integrable quantum model obeys these bilinear functional relations, which are identified with an integrable dynamical system on a Grassmann manifold (higher Hirota equation). The bilinear relations were previously known for a particular class of transfer matrices corresponding to rectangular Young diagrams. We extend this result for general Young diagrams. A general solution of the bilinear equations is presented.

Painting the Phase Space Portrait of an Integrable Dynamical System

Science ◽  
1990 ◽  
Vol 247 (4944) ◽  
pp. 833-836 ◽  
Author(s):  
S. Coffey ◽  
A. Deprit ◽  
E. Deprit ◽  
L. Healy
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Integrable Dynamical System ◽  
Phase Space Portrait
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