Results 31 to 40 of about 1,278,901 (285)

On Separation of Variables for Integrable Equations of Soliton Type [PDF]

, 2007
We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra $\mathfrak{sl}(2,\Complex)\times \mathcal{P}(\lambda,\lambda^{-1})$.
Adler M., Alber M. S., Antonowicz M., Babelon O., Bernatska J. N., Blaszak M., Blaszak M., Blaszak M., Dubrovin B. A., Dubrovin B. A., Falqui G., Falqui G., Falqui G., Harnad J., Holod P., Holod P. I., Holod P. I., Holod P. I., Its A. R., Kac V., Kozel V. A., Magnano G., Novikov S. P., Previato E., Prikarpatsky A. K., Sklyanin E. K., Sklyanin E. K., Sklyanin E. K., ten Kroode F., Veselov A. P., Veselov A. P.   +30 more
core   +2 more sources

The Fourier U(2) Group and Separation of Discrete Variables [PDF]

, 2011
The linear canonical transformations of geometric optics on two-dimensional screens form the group $Sp(4,R)$, whose maximal compact subgroup is the Fourier group $U(2)_F$; this includes isotropic and anisotropic Fourier transforms, screen rotations and ...
Vicent, Luis Edgar, Wolf, Kurt Bernardo
core   +4 more sources

Shape invariance and SUSY separation of variables

EPJ Web of Conferences, 2016
The main ingredients of conventional Supersymmetrical Quantum Mechanics (SUSY QM) are presented. The generalization with supercharges of second order in derivatives - Second Order SUSY - is formulated, and the property of shape invariance is defined. The
Ioffe M.V., Kolevatova E.V., Vereshagin V.   +2 more
doaj   +1 more source

Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)] [PDF]

, 1992
There being no precise definition of the quantum integrability, the separability of variables can serve as its practical substitute. For any quantum integrable model generated by the Yangian Y[sl(3)] the canonical coordinates and the conjugated operators
A. N. Kirillov, B. Jurčo, B. Jurčo, B. Sutherland, C. N. Yang, E. K. Sklyanin, E. K. Sklyanin, E. K. Sklyanin, I. V. Cherednik, M. Gaudin, P. P. Kulish, P. P. Kulish, P. P. Kulish, S. Weigert, V. Chari   +14 more
core   +2 more sources

Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics

Symmetry, Integrability and Geometry: Methods and Applications, 2010
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance -
Mikhail V. Ioffe
doaj   +1 more source

Action-angle variables for the Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation

Frontiers in Physics, 2023
In this work, we present two finite-dimensional Lie–Poisson Hamiltonian systems associated with the Hirota–Satsuma modified Boussinesq equation by using the nonlinearization method. Moreover, the separation of variables on the common level set of Casimir
Xue Geng, Dianlou Du, Xianguo Geng
doaj   +1 more source

Separation of variables for the Ruijsenaars system

, 1997
We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector (Baker-Akhiezer ...
Kuznetsov, V. B., Nijhoff, F. W., Sklyanin, E. K.   +2 more
core   +2 more sources

Spectral simplicity and asymptotic separation of variables [PDF]

, 2010
We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not.
Chris Judge, G. Lamé, J.H. Albert, K. Uhlenbeck, L. Friedlander, L. Hillairet, L. Hillairet, L. Hillairet, Luc Hillairet, M. Harmer, M. Reed, M.A. Pinsky, M.V. Berry, P. Bérard, P. Exner, P. Lax, P. Sarnak, R. Courant, R.E. Langer, T.M. Cherry   +19 more
core   +2 more sources

New Variables of Separation for the Steklov-Lyapunov System

Symmetry, Integrability and Geometry: Methods and Applications, 2012
A rigid body in an ideal fluid is an important example of Hamiltonian systems on a dual to the semidirect product Lie algebra e(3)=so(3)⋉R^3. We present the bi-Hamiltonian structure and the corresponding variables of separation on this phase space for ...
Andrey V. Tsiganov
doaj   +1 more source

Large-signal averaged models of the non-ideal flyback converter derived by the separation of variables [PDF]

Bulletin of the Polish Academy of Sciences: Technical Sciences, 2020
The main topic of the paper is the large signal averaged model of a switch-mode flyback power converter. The use of the large-signal averaged models of switching converters allows for fast simulation of power systems.
W. Janke, M. Bączek, J. Kraśniewski
doaj   +1 more source