Numerical analysis of one-soliton solutions on a Bianchi type-II background

The asymptotic behavior of a solution of vacuum Einstein equations describing the propagation of a single soliton wave on a Bianchi type-II background is investigated numerically. In the framework of the oscillatory approach to a cosmological singularity, the transitional behavior corresponding to a critical value of a fundamental integration constant is analyzed.     

Solitonic solutions on a Bianchi II background generated by SHEEP algebraic manipulation

The exact solutions of Einstein's (vacuum) field equations corresponding to a (real-poles) three-solitonic perturbation of a Bianchi type II space-time are investigated by using computer algebra. Two-dimensional and three-dimensional plots of the relevant solitonic fields are obtained numerically.     

Stationary cosmological Bianchi II solutions

Stationary cosmological solutions for the Bianchi metric II are derived. In the models, use is made of a scalar field with a vacuum-averaged energy-momentum tensor, a cosmological constant, and ideal co-moving or not co-moving liquids as sources of gravitations.     

Curvature properties of real one-pole solitonic perturbations on a Bianchi II background

The curvature properties of the real one-solitonic perturbations on a Bianchi II background found by Belinskii and Francaviglia are studied. The conjectured singularity at spatial infinity is shown to be a pure coordinate effect. New coordinates are introduced that remove some false infinities on the light-cone. A null-fluid shock wave is found to propagate along the light-cone.     

A new family of evolution water-wave equations possessing two-soliton solutions

We find a new family of fifth-order water-wave equations having common invariant manifold of the fourth order. These evolution equations are nonintegrable except for two cases corresponding to the Sawada–Kotera and Kaup–Kupershmidt equations. The invariant manifold of the family is an autonomous equation F-VI from the Cosgrove's classification of fourth-order ODEs having the Painlevé property. Two-parameter solutions of the equation F-VI allow to find two-soliton solutions for this family of evolution equations.     

Soliton dynamics of symmetry-endowed two-soliton solutions of the nonlinear Schrodinger equation

A comprehensive analysis is presented of the propagation of symmetry-endowed two-soliton solutions under the influence of various perturbations important in nonlinear optics. Thus, we begin by introducing the analytical expressions of these two-soliton solutions. Then, by considering perturbations which preserve the initial symmetry of the two-soliton solutions, the dependence of the soliton parameters on the propagation distance is determined by using an adiabatic perturbation method. As perturbations of this kind, important for soliton-based communication systems, we consider the bandwidth-limited amplification, nonlinear amplification, and amplitude and phase modulation. Moreover, the results obtained by the adiabatic perturbation method are compared with those obtained by direct numerical simulations of the corresponding governing differential equations. (c) 2000 American Institute of Physics.     

Noether symmetries of Bianchi type II spacetimes

This paper is devoted to investigate Noether symmetries of Bianchi type II spacetimes. We use the reduced involutive form of the determining equations to classify their possible algebras. We show that Noether symmetries contain both Killing vectors and homothetic motions.     

D-brane solutions in a light-like linear dilaton background

The light-like linear dilaton background presents a simple time dependent solution of type II supergravity equations of motion that preserves 1/2 supersymmetry in ten dimensions. We construct supergravity D-brane solutions in a linear dilaton background starting from the known intersecting brane solutions in string theory. By applying a Penrose limit on the intersecting (NS1–NS5–NS5′)-brane solution, we find out a D5-brane in a linear dilaton background. We solve the Killing spinor equations for the brane solutions explicitly, and show that they preserve 1/4 supersymmetry. We also find a M5-brane solution in eleven-dimensional supergravity.     

Matter collineation classification of Bianchi type II spacetime

In this paper we classified the matter collineations (MCs) of Bianchi type II spacetime according to the degenerate and non-degenerate energy-momentum tensor. It is shown that when the energy-momentum tensor is degenerate, most of the cases yield infinite dimensional MCs whereas some cases give finite dimensional Lie algebras in which there are three, four or five MCs. For the non-degenerate matter tensor cases we obtained that the Lie algebra of MCs is finite dimensional, in which the number of MCs are also three, four or five. Furthermore, we discussed the physical implications of the obtained MCs in the case of perfect fluid as source.     

Absence of preclassical solutions in Bianchi I loop quantum cosmology

Loop quantum cosmology, the symmetry reduction of quantum geometry for the study of various cosmological situations, leads to a difference equation for its quantum evolution equation. To ensure that solutions of this equation act in the expected classical manner far from singularities, additional restrictions are imposed on the solution. In this Letter, we consider the Bianchi I model, both the vacuum case and the addition of a cosmological constant, and show using generating function techniques that only the zero solution satisfies these constraints. This implies either that there are technical difficulties with the current method of quantizing the evolution equation, or else loop quantum gravity imposes strong restrictions on the physically allowed solutions.     

Some exact solutions of string cosmology in Bianchi III space-time

Following the techniques used by Letelier and Stachel some exact Bianchi III cosmological solutions of massive strings in the presence of magnetic field are obtained and their physical features are discussed. Some string solutions in which magnetic fields are absent are also discussed.     

On Bianchi type-I vacuum solutions inR+R 2 theories of gravitation. II. The axially symmetric anisotropic case

The field equations following from a LagrangianL(1/L)(–g)^1/2[(1/2)R+l ²(R _lk R ^lk +R ²)] will be considered for Bianchi type-I homogeneous models. Thereby the special case,+3=0, is considered qualitatively for axially symmetric anisotropic metrics. Generically, the solutions have both past and future singularities, but it will be proven by topological arguments that the two-dimensional space of solutions possesses a one-parameter subspace of solutions with a behavior similar to the Kasner solution.     

Qualitative analysis of a class of Bianchi VI0 imperfect fluid cosmologies

A set of dimensionless equations of state is used to show that the Einstein field equations governing a class of Bianchi VI₀ imperfect fluid cosmologies reduce to a plane-autonomous system of equations. The qualitative behavior of the underlying cosmological models is obtained by investigating this plane-autonomous system.     

Bianchi type-I string cosmological model in the presence of a magnetic flux: exact and qualitative solutions

A Bianchi type-I cosmological model in the presence of a magnetic flux along a cosmological string is investigated. The objective of this study is to generate solutions to the Einstein equations using a few tractable assumptions usually accepted in the literature. The analytical solutions are supplemented with numerical and qualitative analysis. In the frame of the present model the evolution of the Universe and other physical aspects are discussed.     

Zero-curvature FRW models and Bianchi I space-time as solutions of the same equation

We show that the condition of isotropy of pressure in the case of Bianchi I space-time filled with a perfect fluid reduces via a suitable scale transformation to a linear second-order differential equation, which admits as particular solutions those of Friedmann, Robertson, and Walker. These particular solutions are then used for generating many new local rotational symmetry Bianchi I solutions. Some of their physical properties are then studied.     

Global existence of solutions for the relativistic Boltzmann equation with arbitrarily large initial data on a Bianchi Type I space-time

We prove, for the relativistic Boltzmann equation on a Bianchi Type I space-time, a global existence and uniqueness theorem, for arbitrarily large initial data.