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.     

Soliton solutions for the space-time nonlinear partial differential equations with fractional-orders

Many practical models in interdisciplinary fields can be described with the help of fractional-order nonlinear partial differential equations(NPDEs). Fractional-order NPDEs such as the space-time fractional Fokas equation, the space-time Kaup–Kupershmidt equation and the space-time fractional (2+1)-dimensional breaking soliton equation have been widely applied in many branches of science and engineering. So, finding exact traveling wave solutions are very helpful in the theories and numerical studies of such equations. More precisely, fractional sub-equation method together with the proposed technique is implemented to obtain exact traveling wave solutions of such physical models involving Jumarie’s modified Riemann–Liouville derivative. As a result, some new exact traveling wave solutions for them are successfully established. Also, (1+1)-dimensional plots and 1-dimensional plots of some of the derived solutions are given to visualize the dynamics of the considered NPDEs. The obtained results reveal that the proposed technique is quite effective and convenient for obtaining exact solutions of NPDEs with fractional-order.     

Superfield approach to the construction of effective action in quantum field theory with extended supersymmetry

We review the current state of research on the construction of effective actions in supersymmetric quantum field theory. Special attention is paid to gauge models with extended supersymmetry in the superfield approach. The advantages of formulation of such models in harmonic superspace for the calculation of effective action are emphasized. Manifestly supersymmetric and manifestly gauge-invariant methods for constructing the low-energy effective actions and deriving the corrections to them are considered and the possibilities to obtain the exact solutions are discussed. The calculations of one-loop effective actions in N = 2 supersymmetric Yang–Mills theory with hypermultiplets and in N = 4 supersymmetric Yang–Mills theory are analyzed in detail. The relationship between the effective action in supersymmetric quantum field theory and the low-energy limit in superstring theory is discussed.     

Inferences concerning the real part of the heavy-ion optical potential through folding techniques

Analytic solutions are given for the real part of the heavy-ion optical potential through the use of single and double folding models. The effective potential between the nucleons is in the form of a sum of Yukawa terms and the distributions of the densities and the nucleon optical potential are taken to be of Woods-Saxon form. Consideration is given to the influence of the tails of the density distribution as well as that of the effective potential. Calculations suggest there is little need to delineate effective interactions with momentum components much beyond the Fermi level. This provides a rationale for realistic treatments of the effective interaction. A crucial parameter specifying the density distribution is found to be the rms radius.     

Harmonic wave propagation in materials with periodic beam-structure

The characteristics of harmonic waves propagating in periodic beam structures are investigated. For this purpose, a very effective method for the calculation of dispersion relations of elastic waves in these materials is developed by applying dynamic theory of crystal lattices to discrete models of periodic beam structures. This method is applicable to general three-dimensional periodic beam structures. Results presented show that the solutions converge to the exact solution as the number of atoms in the discrete models increases. The dispersion relations of plane harmonic waves in the micropolar continuum model, developed in a previous study, are also calculated. They are compared with the exact solutions to examine the applicability of the continuum models to dynamic problems.     

Comparative analysis of approximate and exact models in inflationary cosmology

A method of constructing and analyzing exact solutions for inflationary cosmology models with a self-action scalar by introducing an effective self-action potential is suggested. On the basis of exact solutions for complete and “shortened” equations obtained in the “slow-descent” approximation, their comparative analysis is made. It is shown that the results obtained for approximate models that are conventionally used for comparison with experimental data may differ greatly from those for exact models because of the structural instability of models with inflation. Ul'anovsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 14–20, January, 2000.     

New Optical Soliton Solutions of Nolinear Evolution Equation Describing Nonlinear Dispersion

In this work, we examine two algorithm schemes, namely, Kudryashov expansion andAuxiliary equation method for obtaining new optical soliton solutions of the discreteelectrical lattice models in nonlinear scheme (Salerno equation). Our solutions obtainedhere are include the hyperbolic, rational, and trigonometric functions. Our two used methods are proved to be effective and powerful methods in obtaining the exact solutions of nonlinearevolution equations (NLEEs).     

Exact travelling wave solutions for some important nonlinear physical models

The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.     

Construction of solitary solutions for nonlinear dispersive equations by variational iteration method

Variational iteration method is implemented to construct solitary solutions for nonlinear dispersive equations. In this scheme the solution takes the form of a convergent series with easily computable components. The chosen initial solution or trial function plays a major role in changing the physical structure of the solution. Many models are approached and the obtained results reveal that the method is very effective and convenient for constructing solitary solutions.     

Meeting the constraint of neutrino—Higgsino mixing in gravity unified theories

In gravity unified theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B - L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.     

Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation on manifolds enabled with nonholonomic distributions is considered. We prove that, for certain types of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic noncommutative gravity theories models and analyzed the stability of stationary ellipsoidal solutions defining some nonholonomic and/or nonsymmetric deformations of the Schwarzschild metric. We show how to construct nonholonomic distributions which remove instabilities in nonsymmetric gravity theories. It is concluded that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of some models and/or unconstrained solutions.     

Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.     

Off-shell photon distribution amplitudes in the low-energy effective theory of QCD

The mechanism of the initial inflationary scenario of the Universe and of its late-time acceleration can be described by assuming the existence of some gravitationally coupled scalar fields $\phi $ , with the inflaton field generating inflation and the quintessence field being responsible for the late accelerated expansion. Various inflationary and late-time accelerated scenarios are distinguished by the choice of an effective self-interaction potential $V(\phi )$ , which simulates a temporarily non-vanishing cosmological term. In this work, we present a new formalism for the analysis of scalar fields in flat isotropic and homogeneous cosmological models. The basic evolution equation of the models can be reduced to a first-order non-linear differential equation. Approximate solutions of this equation can be constructed in the limiting cases of the scalar-field kinetic energy and potential energy dominance, respectively, as well as in the intermediate regime. Moreover, we present several new accelerating and decelerating exact cosmological solutions, based on the exact integration of the basic evolution equation for scalar-field cosmologies. More specifically, exact solutions are obtained for exponential, generalized cosine hyperbolic, and power-law potentials, respectively. Cosmological models with power-law scalar field potentials are also analyzed in detail.     

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.     

Nonlinear chiral models: Soliton solutions and spatio-temporal chaos

Nonlinear effective Lagrangian models with a chiral symmetry have been used to describe strong interactions at low energy, for a long time. The Skyrme model and the chiral quark-meson model are two such models, which have soliton solutions which can be identified with the baryons. We describe the various kinds of soliton states in these nonlinear models and discuss their physical significance and uses in this review. We also study these models from the view point of classical nonlinar dynamical systems. We consider fluctuations around theB=1 soliton solutions of these models (B, being the baryon number) and solve the spherically symmetric, time-dependent systems. Numerical studies indicate that the phase space around the Skyrme soliton solution exhibits spatio-temporal chaos. It is remarkable that topological solitons signifying stability/order and spatio-temporal chaos coexist in this model. In contrast with this, the soliton of the quark-meson model is stable even for large perturbations.     

Solitons and Vortices in Plasmas

The various types of nonlinear wave solutions in plasmas are reviewed. First, the generation, pro- pagation, and stability of solitary waves are demonstrated for some simple examples. Then, relevant two-and three-dimensional models for Langniuir solitons are proposed and investigated. The collapse as an effective dissipation mechanism in plasmas is discussed in detail. Finally, simple models of two-dimensional vortex motion and their consequences are considered.     

An analysis of the three-valence model of photorefraction

In this paper we present an analysis of the three-valence model of photorefraction. The basic equations of the model are studied and solved to find zero- and first-order solutions in the steady state, including expressions for the space-charge field and the effective trap density. The intensity dependence of the solutions for the population densities and space-charge field are analysed and discussed for varying proportions of the different valence states in the material, and the influence of some important material parameters considered. The possible applications of these results to the experimental characterisation of three-valence-state materials are discussed and some comparisons are made between the three-valence and the two-independent-centre models of photorefraction. Received: 17 November 1998 / Revised version: 8 January 1999 / Published online: 31 March 1999     

Analytical solutions of exact renormalization group equations

We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of physical behaviour such as fixed points governing the universal behaviour near second-order phase transitions, critical exponents, first-order transitions (some of which are radiatively induced) and tricritical behaviour.     

Closed form soliton solutions of three nonlinear fractional models through proposed improved Kudryashov method

We introduce a new integral scheme namely improved Kudryashov method for solving any nonlinear fractional differential model. Specifically, we apply the approach to the nonlinear space–time fractional model leading the wave to spread in electrical transmission lines(s-tf ETL), the time fractional complex Schr?dinger(tfc S), and the space–time M-fractional Schr?dinger–Hirota(s-t M-f SH) models to verify the effectiveness of the proposed approach. The implementing of the introduced new technique based on the models provides us with periodic envelope, exponentially changeable soliton envelope, rational rogue wave, periodic rogue wave, combo periodic-soliton, and combo rational-soliton solutions, which are much interesting phenomena in nonlinear sciences. Thus the results disclose that the proposed technique is very effective and straight-forward, and such solutions of the models are much more fruitful than those from the generalized Kudryashov and the modified Kudryashov methods.     

New representation of the nonlocal ghost-free gravity theory

A new representation is found for the action of the recently suggested ghost-free nonlocal gravity models generating de Sitter or Anti-de Sitter background with an arbitrary value of the effective cosmological constant. This representation allows one to extend applications of these models from maximally symmetric to generic Einstein spaces and black hole solutions, but clearly indicates violation of the general relativistic limit in this class of theories, induced by their infrared behavior. It is shown that this limit can be recovered in a special conformal frame of these theories, and their relation to critical gravity models is also briefly discussed.