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Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

100%
Wang C.-Y., Gui Y.-X., Gao Y.-J.
Open Physics
|
2008
|
vol. 6
|
issue 3
462-468
EN
We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.
2
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Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

84%
Ikhdair S., Sever R.
Open Physics
|
2008
|
vol. 6
|
issue 3
685-696
EN
A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $$ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} $$. The energy eigenvalues and eigenfunctions of the bound-states for the Schrödinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.
3
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Inverse scattering method and soliton double solution family for string effective action

84%
Gao Y.-J.
Open Physics
|
2009
|
vol. 7
|
issue 4
821-828
EN
A so-called modified Hauser-Ernst-type extended double-complex linear system is established and used to develop a new inverse scattering method for solving the equations of motion of the string effective action describing the coupled gravity, dilaton and Kalb-Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the application of the inverse scattering method fine and effective. As an application, a concrete family of soliton double solutions for the considered theory is obtained.
4
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Unification Principle and a Geometric Field Theory

84%
Wanas M. I., Osman S. N., El-Kholy R. I.
Open Physics
|
2015
|
vol. 13
|
issue 1
EN
In the context of the geometrization philosophy, a covariant field theory is constructed. The theory satisfies the unification principle. The field equations of the theory are constructed depending on a general differential identity in the geometry used. The Lagrangian scalar used in the formalism is neither curvature scalar nor torsion scalar, but an alloy made of both, the W-scalar. The physical contents of the theory are explored depending on different methods. The analysis shows that the theory is capable of dealing with gravity, electromagnetism and material distribution with possible mutual interactions. The theory is shown to cover the domain of general relativity under certain conditions.
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