LRS Bianchi type I perfect fluid solutions generated from known solutions

Some LRS Bianchi type I perfect fluid solutions are generated from known solutions of this type. The solutions represent spatially homogeneous and anisotropic cosmological models which would give essentially empty space for large time. The physical and kinematic properties of the models are discussed.     

Charged Noncommutative Wormhole Solutions via Power-Law f(T) Models

In this paper, we explore static spherically symmetric charged wormhole solutions in extended teleparallel gravity taking power-law f(T) models. We consider noncommutative geometry under Lorentzian distribution. In order to obtain matter components, we develop field equations using effective energy-momentum tensor for non-diagonal tetrad. We explore solutions by considering various viable power-law f(T) models, which also include teleparallel gravity case. The violation of energy conditions obtain by exotic matter to form wormhole solutions in teleparallel case while, physical acceptable wormhole solutions exist for charged noncommutative wormhole solutions for some cases of power-law models. The effective energy-momentum tensor and charge are responsible for the violation of the energy conditions. Also, we check the equilibrium condition for these solutions. The equilibrium condition meets for the teleparallel case and some power-law solutions while remaining solutions are either in less equilibrium or in disequilibrium situation.     

Mathematical Models for the Propagation of Stress Waves in Elastic Rods: Exact Solutions and Numerical Simulation

In this work, the Bishop and Love models for longitudinal vibrations are adopted to study the dynamics of isotropic rods with conical and exponential cross-sections. Exact solutions of both models are derived, using appropriate transformations. The analytical solutions of these two models are obtained in terms of generalised hypergeometric functions and Legendre spherical functions respectively. The exact solution of Love model for a rod with exponential cross-section is expressed as a sum of Gauss hypergeometric functions. The models are solved numerically by using the method of lines to reduce the original PDE to a system of ODEs. The accuracy of the numerical approximations is studied in the case of special solutions.     

Compactons versus solitons

We investigate whether the recently proposed PT-symmetric extensions of generalized Korteweg-de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which is independent of their amplitude and those which possess unstable compacton solutions the Painlevé test fails, such that no soliton solutions can be found. The Painlevé test is passed for models allowing for compacton solutions whose width is determined by their amplitude. Consequently, these models admit soliton solutions in addition to compactons and are integrable.     

Absence of static solutions in source-free Yang-Mills theory

The vanishing of self-stress for static systems excludes finite energy time-independent solutions of source-free Yang-Mills models (with compact gauge groups), except in five dimensions. Static solutions of Abelian self-interacting models of the Born-Infeld type are also forbidden.     

Field-theoretic extended particles in two space dimensions

A family of Lagrangian models of two scalar fields in (2 + 1) dimensions is studied. All their localized static classical solutions are obtained, and interpreted as representing systems of extended particles. The models are generalized by taking into account general-relativistic gravirational coupling, for which case the general static solutions are also obtained explicitly.     

Generation of LRS Bianchi type I universes filled with perfect fluids

A generating technique is presented which converts known LRS Bianchi type I models into new models of the same type. Starting from the general Kasner solutions new classes of models are obtained which add to the rare perfect-fluid solutions not satisfying the equation of state. The physical and kinematical properties of cosmological models are studied.     

Universality of the linear potential in effective models for the low energy QCD coupled with the dilaton field

QCD motivated effective models coupled with the cosmological dilaton field are analyzed. It is shown that all models possess confining solutions with the linear potential of confinement even thought such solutions are not observed in the original effective theory. In case of the Pagels–Tomboulis model analytical solutions are explicit found.     

Pure Kinetic K-essence as the Cosmic Speed-Up

In this paper, we consider three types of k-essence. These k-essence models were presented in the parametric forms. The exact analytical solutions of the corresponding equations of motion are found. It is shown that these k-essence models for the presented solutions can give rise to cosmic acceleration.     

Some Generalized Scalar Field Models with Abundant Soliton-Like configurations

Some generahed scalar field models are presented. It is shown that there exist generally three types of soliton solutions for the extended models. The form of the first type of the soliton solutions is model-independent. An arbitrary constant can be included in the second type of the soliton excitations which is model-dependent. The third type of the soliton solutions is also modeldependent but with no arbitrary constant. The extended φ⁴ model and sine-Gordon model are studied in detail.     

Bianchi Type V Cosmological Models with Constant Deceleration Parameter in General Relativity

We investigate Bianchi type V cosmological models with bulk viscous fluid source. Exact solutions of the Einstein field equations are presented via a suitable power law assumption for the Hubble parameter. We show that the corresponding solutions retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Some observational parameters for the models have also been discussed.     

Isotropization of solutions of the Einstein–Vlasov system with Bianchi V symmetry

Using the methods developed for different Bianchi class A cosmological models we treat the simplest Bianchi class B model, namely Bianchi type V. The future non-linear stability for solutions of the Einstein–Vlasov system is demonstrated and it is shown that these solutions are asymptotically stable to the Milne solution. Within the isotropic solutions of the Einstein–Vlasov system the spatially flat Friedmann solution is unstable within this class, and expanding models tend also to the Milne solution.     

Einige Lösungen der Einsteinschen Feldgleichungen mit idealer Flüssigkeit,die sich in einen fünfdimensionalen flachen Raum einbetten lassen

All solutions of the Einstein equations for a perfect fluid are given, which are invariantly characterized by: embedding class one, Petrov typeD, zero acceleration of matter. Among these solutions are inhomogeneous cosmological models and special solutions with spherical symmetry.     

Geodesic Bianchi type cosmological models

Some perfect fluid solutions of Einstein's field equations are obtained in spacetimes with two hypersurface orthogonal space-lika commuting Killing vectors. The flow is assumed to be geodesic. The solutions depend on an arbitrary function of time which determines the equation of state. In the models derived one additional Killing vector exists and the solutions are actually Bianchi-type cosmological models.     

Generalized Chaplygin Gas Dominated Anisotropic Bianchi Type-I Cosmological Models

We present Bianchi type-I cosmological models in the presence of generalized Chaplygin gas and perfect fluid for early and late time epochs. Exact solutions of Einstein’s field equations for this model are obtained. The general solutions of gravitational field equations are expressed in an exact parametric form, with average scale factor as parameter. In the limiting cases of small and large values of the average scale factor, the solutions of the field equations are expressed in exact analytic forms. Moreover, this model predicts that the expansion of Universe is accelerating for the late times. The physical and geometrical properties of the corresponding cosmological models are discussed.     

2+1-dimensional gravitational decoupled anisotropic solutions

This paper investigates exact models for spherically symmetric anisotropic matter distribution in 2+1-dimensions via gravitational decoupling approach. For this purpose, we choose known spherical solutions with perfect fluid in the absence as well as the presence of cosmological constant and extend them to anisotropic models by imposing a constraint on matter components. The physical viability and stability of our developed solutions are investigated through graphical analysis of density, radial/tangential pressure, energy conditions, and causality criterion. It is found that both solutions are stable and satisfy all the physical requirements for the feasible choice of the model parameters.     

Exact (1+1)-dimensional solutions of discrete planar velocity Boltzmann models

For discrete velocity Boltzmann models we have found (1+1)-dimensional shock waves and periodic solutions that are rational solutions with two exponential variables exp(_ix + _it) (spacex, timet). These exact solutions are sums of two rational solutions, each with one exponential variable (similarity solutions). We study the planar velocity models and explicitly write the results for the square 4-velocity and the hexagonal 6-velocity models introduced by Gatignol.     

General properties of geophysical hydrodynamics models

The influence of simplifying assumptions used in geophysical hydrodynamics models on the general properties of space and time, as well as on the fundamental physical principles that underlie the mechanical systems, is studied. Analysis of the general properties of such models is supplemented by investigation of the peculiarities introduced by stratification into the solutions of nonlinear stationary models. The possibilities for representing the solutions as finite and infinite Fourier series in cylindrical coordinates are explored.     

New classes of exact solutions for magnetic reconnective annihilation

Analytical solutions for reconnective annihilation in curvilinear geometry are presented. These solutions are characterized by current density distributions varying both along the radial and azimuthal coordinates. They represent an extension of previously proposed models, based on purely radially dependent current densities. Possible applications of these solutions to the modeling of solar flares are also discussed.     

A class of cylindrically-symmetric models in string cosmology

A new class of physically relevant explicit solutions for string cosmological models endowed with cylindrical symmetry on the background of singularity-free cosmological space times has been obtained and their physical and kinematical features are discussed. The matter-free limits of this class of solutions are observed to be the singularity-free vacuum solutions of Patel and Dadhich.