Discrete symmetries and nonlocal reductions

Pekcan, Asli
Zheltukhın, Kostyantyn
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.


Effective Mass Schrodinger Equation via Point Canonical Transformation
Arda, Altug; Sever, Ramazan (IOP Publishing, 2010-07-01)
Exact solutions of the effective radial Schrodinger equation are obtained for some inverse potentials by using the point canonical transformation. The energy eigenvalues and the corresponding wave functions are calculated by using a set of mass distributions.
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...
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.
On a transformation between hierarchies of integrable equations
GÜRSES, METİN; Zheltukhın, Kostyantyn (Elsevier BV, 2006-02-20)
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.
Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
Egrifes, H; Sever, Ramazan (Elsevier BV, 2005-09-05)
The one-dimensional Dirac equation is solved for the PT-symmetric generalized Hulthen potential. The Nikiforov-Uvarov method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions.
Citation Formats
M. GÜRSES, A. Pekcan, and K. Zheltukhın, “Discrete symmetries and nonlocal reductions,” PHYSICS LETTERS A, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37667.