Geometrization of the Lax pair tensors

Baleanu, D
Baskal, S
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.


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We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term K. We also investigate the energ...
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The algebra of observables of planar electrons subject to a constant background magnetic field B is given by A(theta)(R-2) circle times A(theta)(R-2) (theta = -4/eB), the product of two mutually commuting Moyal algebras. It describes the free Hamiltonian and the guiding center coordinates. We argue that A(theta)(R-2) itself furnishes a representation space for the actions of these two Moyal algebras, and suggest physical arguments for this choice of the representation space. We give the proper setup to coup...
Citation Formats
D. Baleanu and S. Baskal, “Geometrization of the Lax pair tensors,” MODERN PHYSICS LETTERS A, pp. 1503–1510, 2000, Accessed: 00, 2020. [Online]. Available: