On a transformation between hierarchies of integrable equations

Download
2006-02-20
GÜRSES, METİN
Zheltukhın, Kostyantyn
A transformation between a hierarchy of integrable equations arising from the standard R-matrix construction on the algebra of differential operators and a hierarchy of integrable equations arising from a deformation of the standard R-matrix is given.
PHYSICS LETTERS A

Suggestions

Discrete symmetries and nonlocal reductions
GÜRSES, METİN; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-01-31)
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
Exact solution of the Klein-Gordon equation for the PT-symmetric generalized Woods-Saxon potential by the Nikiforov-Uvarov method
Ikhdair, Sameer M.; Sever, Ramazan (Wiley, 2007-03-01)
The exact solution of the one-dimensional Klein-Gordon equation of the PT-symmetric generalized Woods-Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s-states are also investigated for different types of complex generalized Woods-Saxon potentials. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit
Aydogdu, Oktay; Sever, Ramazan (Elsevier BV, 2010-02-01)
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...
Approximate analytical solutions of the pseudospin symmetric Dirac equation for exponential-type potentials
Arda, Altu; Sever, Ramazan; TEZCAN, CEVDET (Wiley, 2009-10-01)
The solvability of The Dirac equation is studied for the exponential-type potentials with the pseudospin symmetry by using the parametric generalization of the Nikiforov-Uvarov method. The energy eigenvalue equation, and the corresponding Dirac spinors for Morse, Hulthen, and q-deformed Rosen-Morse potentials are obtained within the framework of an approximation to the spin-orbit coupling term, so the solutions are given for any value of the spin-orbit quantum number kappa = 0, or kappa not equal 0. (C) 200...
Anti-de Sitter-Wave Solutions of Higher Derivative Theories
GÜRSES, METİN; Hervik, Sigbjorn; Sisman, Tahsin Cagri; Tekin, Bayram (American Physical Society (APS), 2013-09-05)
We show that the recently found anti-de Sitter (AdS)-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and type-N traceless Ricci tensors.
Citation Formats
M. GÜRSES and K. Zheltukhın, “On a transformation between hierarchies of integrable equations,” PHYSICS LETTERS A, pp. 37–40, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43594.