Tracking down localized modes in PT-symmetric Hamiltonians under the influence of a competing nonlinearity

The relevance of parity and time reversal (PT)-symmetric structures in optical systems is known for sometime with the correspondence existing between the Schrodinger equation and the paraxial equation of diffraction where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrodinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation charaterized by the parameter of perturbative growth rate passing through zero where a transition to imaginary eigenvalues occurs.Comment: 10pages, To be published in Acta Polytechnic

TRACKING DOWN LOCALIZED MODES IN PTSYMMETRIC HAMILTONIANS UNDER THE INFLUENCE OF A COMPETING NONLINEARITY

The relevance of parity and time reversal (PT)-symmetric structures in optical systems has been known for some time with the correspondence existing between the Schrödinger equation and the paraxial equation of diffraction, where the time parameter represents the propagating distance and the refractive index acts as the complex potential. In this paper, we systematically analyze a normalized form of the nonlinear Schrödinger system with two new families of PT-symmetric potentials in the presence of competing nonlinearities. We generate a class of localized eigenmodes and carry out a linear stability analysis on the solutions. In particular, we find an interesting feature of bifurcation characterized by the parameter of perturbative growth rate passing through zero, where a transition to imaginary eigenvalues occurs

Physical approach to cosmological homogeneity

This paper shows that in general relativity space-time will admit three linearly independent spacelike Killing vectors if the cosmic matter is a perfect fluid with a functional relationship between pressure and density and the spacelike eigenvectors of the shear tensor are parallel transported along the world lines of the fluid. In the Newtonian case it is proved that for an irrotational motion of a fluid with pressure and density functionally related spatial uniformity of the matter distribution leads to the homogeneity of the velocity field