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

New conserved tensors and Brans–Dicke-type field equation, using integrability condition

In this paper, we explore some new off-shell and on-shell conserved quantities for a scalar field in Minkowski space, using integrability condition. The off-shell conserved tensors are related to the kinematics of the field, while a linear combination of the off-shell and the on-shell conserved tensors ends up with the energy–momentum tensor for the scalar field. In the curved background, using Ricci and Bianchi identities, scalar–tensor theory of gravity, that resembles somewhat with Brans–Dicke-type field equations, emerges without requiring the principle of equivalence. Further, starting from the curvature scalar and using these identities, the field equations for modified gravity (Einstein–Hilbert action in the presence of higher-order terms) follow. </jats:p

Nonstandard Lagrangians and branching: The case of some nonlinear Liénard systems

We propose a new form of Lagrangian that shows branching for the associated Hamiltonian and has relevance to the quadratic type and mixed linear-quadratic Liénard-type nonlinear dynamical equations on adjusting the underlying parameters. Non-uniqueness of the Lagrangian is pointed out and a particular one when Fourier transform is demonstrated to depict a momentum-dependent quantum-like mass system when expanded binomially. </jats:p