Optical solitons and other solutions to the conformable space–time fractional complex Ginzburg–Landau equation under Kerr law nonlinearity

This study reveals the dark, bright, combined dark–bright, singular, combined singular optical solitons and singular periodic solutions to the conformable space–time fractional complex Ginzburg–Landau equation. We reach such solutions via the powerful extended sinh-Gordon equation expansion method (ShGEEM). Constraint conditions that guarantee the existence of valid solitary wave solutions are given. Under suitable choice of the parameter values, interesting three-dimensional graphs of some of the obtained solutions are plotted.     

Geometrical locus of massive test particle orbits in the space of physical parameters in Kerr space–time

Gravitational radiation of binary systems can be studied by using the adiabatic approximation in General Relativity. In this approach a small astrophysical object follows a trajectory consisting of a chained series of bounded geodesics (orbits) in the outer region of a Kerr Black Hole, representing the space time created by a bigger object. In our paper, we study the entire class of orbits, both of constant radius (spherical orbits), as well as non-null eccentricity orbits, showing a number of properties on the physical parameters and trajectories. The main result is the determination of the geometrical locus of all the orbits in the space of physical parameters in Kerr space–time. This becomes a powerful tool to know if different orbits can be connected by a continuous change of their physical parameters. A discussion on the influence of different values of the angular momentum of the hole is given. Main results have been obtained by analytical methods.     

Generalised space–time and duality

In this Letter we consider the previously proposed generalised space–time and investigate the structure of the field theory upon which it is based. In particular, we derive a SO(D,D)$\mathit{SO}(D,D)$ formulation of the bosonic string as a non-linear realisation at lowest levels of E₁₁s_⊗l₁$E_{11}{\otimes }_s{l}_1$ where l₁$l_1$ is the first fundamental representation. We give a Hamiltonian formulation of this theory and carry out its quantisation. We argue that the choice of representation of the quantum theory breaks the manifest SO(D,D)$\mathit{SO}(D,D)$ symmetry but that the symmetry is manifest in a non-commutative field theory. We discuss the implications for the conjectured E₁₁$E_{11}$ symmetry and the role of the l₁$l_1$ representation.     

Peregrine solitons and gradient catastrophes in discrete nonlinear Schrödinger systems

In the present work, we examine the potential robustness of extreme wave events associated with large amplitude fluctuations of the Peregrine soliton type, upon departure from the integrable analogue of the discrete nonlinear Schrödinger (DNLS) equation, namely the Ablowitz–Ladik (AL) model. Our model of choice will be the so-called Salerno model, which interpolates between the AL and the DNLS models. We find that rogue wave events are drastically distorted even for very slight perturbations of the homotopic parameter connecting the two models off of the integrable limit. Our results suggest that the Peregrine soliton structure is a rather sensitive feature of the integrable limit, which may not persist under “generic” perturbations of the limiting integrable case.     

Spinning particles in Schwarzschild–de Sitter space–time

After considering the reference case of the motion of spinning test bodies in the equatorial plane of the Schwarzschild space–time, we generalize the results to the case of the motion of a spinning particle in the equatorial plane of the Schwarzschild–de Sitter space–time. Specifically, we obtain the loci of turning points of the particle in this plane. We show that the cosmological constant affect the particle motion when the particle distance from the black hole is of the order of the inverse square root of the cosmological constant.     

Stabilization of the Peregrine soliton and Kuznetsov–Ma breathers by means of nonlinearity and dispersion management

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov–Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.     

Condensation and evolution of a space–time network

In this work, we try to propose in a novel way, using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of a space–time network described by the Loop quantum gravity. Considering quantum network connectivity features in Loop quantum gravity, we introduce a link operator, and through extending the dynamical equation for the evolution of the quantum network posed by Ginestra Bianconi to an operator equation, we get the solution of the link operator. This solution is relevant to the Hamiltonian of the network, and then is related to the energy distribution of network nodes. Showing that tremendous energy distribution induces a huge curved space–time network may indicate space time condensation in high-energy nodes. For example, in the case of black holes, quantum energy distribution is related to the area, thus the eigenvalues of the link operator of the nodes can be related to the quantum number of the area, and the eigenvectors are just the spin network states. This reveals that the degree distribution of nodes for the space–time network is quantized, which can form space–time network condensation. The black hole is a sort of result of space–time network condensation, however there may be more extensive space–time network condensations, such as the universe singularity (big bang).     

Gravitational collapse in higher dimensional Husain space–time

We investigate exact solution in higher dimensional Husain model for a null fluid source with pressure p and density ρ are related by the following relations (i) p  =  kρ, (ii) (variable modified Chaplygin) and (iii) p  =  kρ^α (polytropic). We have studied the nature of singularity in gravitational collapse for the above equations of state and also for different choices of the of the parameters k and B namely, (i) k  =  0, B  =  constant (generalized Chaplygin), (ii) B  =  constant (modified Chaplygin). It is found that the nature of singularity is independent of these choices of different equation of state except for variable Chaplygin model. Choices of various parameters are shown in tabular form. Finally, matching of Szekeres model with exterior Husain space–time is done.     

The Riemann tensor and the Bianchi identity in 5D space–time

The initial assumption of theories with extra dimension is based on the efforts to yield a geometrical interpretation of the gravitation field. In this paper, using an infinitesimal parallel transportation of a vector, we generalize the obtained results in four dimensions to five-dimensional space–time. For this purpose, we first consider the effect of the geometrical structure of 4D space–time on a vector in a round trip of a closed path, which is basically quoted from chapter three of Ref. [5]. If the vector field is a gravitational field, then the required round trip will lead us to an equation which is dynamically governed by the Riemann tensor. We extend this idea to five-dimensional space–time and derive an improved version of Bianchi's identity. By doing tensor contraction on this identity, we obtain field equations in 5D space–time that are compatible with Einstein's field equations in 4D space–time. As an interesting result, we find that when one generalizes the results to 5D space–time, the new field equations imply a constraint on Ricci scalar equations, which might be containing a new physical insight.     

Relativistic spin-zero bosons in a Som–Raychaudhuri space–time

We investigate the Duffin–Kemmer–Petiau equation for spin-zero bosons in a (\(3+1\))-dimensional Som–Raychaudhuri space–time. We establish the covariant Duffin–Kemmer–Petiau equation in this curved space–time for the so-called oscillator and we include interaction with a scalar potential. We determine eigenfunctions and the corresponding eigenvalues for the oscillator with the Cornell potential. We investigate the effect of the space–time’s parameters, oscillator’s frequency and the Cornell potential’s parameters on the wave functions.     

Fundamental and dressed annular solitons in saturable nonlinearity with parity–time symmetric Bessel potential

We theoretically study the existence and stability of optical solitons in saturable nonlinearity with a two-dimensional parity–time(PT) symmetric Bessel potential.Besides the fundamental solitons,a novel type of dressed soliton,whose intensity looks like a ring dressed on an intensity hump,are presented.It is found that both the fundamental solitons and dressed solitons can exist when the propagation constant is beyond a certain critical value.The propagation stability is investigated with a linear stability analysis corroborated by a beam propagation method.All the fundamental solitons are stable,while dressed solitons are unstable for low values of saturable parameter.As the value of saturable parameter increases,the dressed solitons tend to be stable at high powers.     

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.     

Grey–grey separate spatial soliton pairs in a biased series photorefractive polymer circuit

Grey–grey separate spatial soliton pairs are predicted in a biased series circuit consisting of two guest-host photorefractive polymers. The numerical results show that two grey solitons in a soliton pair can affect each other by the light-induced current.     

Spherically symmetric solution in a space–time with torsion

By using the method of group analysis, we obtain a new exact evolving and spherically symmetric solution of the Einstein–Cartan equations of motion, corresponding to a space–time threaded with a three-form Kalb–Ramond field strength. The solution describes in its more generic form, a space–time which scalar curvature vanishes for large distances and for large time. In static conditions, it reduces to a classical wormhole solution and to a exact solution with a localized scalar field and a torsion kink, already reported in literature. In the process we have found evidence towards the construction of more new solutions.     

Gap and dark solitons in discrete photorefractive media with?intensity-resonant nonlinearity

Light propagation in one-dimensional nonlinear waveguide arrays with self-defocusing intensity-resonant nonlinearity is investigated theoretically. We study thoroughly conditions for existence and stability of both gap and discrete dark solitons. According to the linear stability analysis both fundamental types (on-site and intersite) of gap solitons may be stable. Discrete dark solitons are unstable except in the low-power regime and, depending on system parameters, evolve into either gray solitons, breathers, or background radiation. Mobility of these solitons is analyzed by the free energy concept: gap solitons are immobile but dark solitons can be easily set in motion.     

Temperature effects of Hamiltonian dark solitons on the stability of holographic solitons in a separate holographic–Hamiltonian soliton pair

We investigate theoretically the temperature effects on the evolution and stability of a separate holographic–Hamiltonian dark–dark or bright–dark soliton pair formed in an unbiased serial photorefractive crystal circuit. Our numerical results show that, for a stable dark–dark or bright–dark soliton pair originally formed in a crystal circuit at given temperatures, when the crystal in which formed a Hamiltonian dark soliton changes, the holographic dark or bright soliton supported by the other crystal tends to evolve into another stable soliton or experiences larger cycles of compression or breaks up into beam filaments or exhibit a common decaying process. The holographic dark soliton is more sensitive to the temperature change than the holographic bright one.     

Null geodesics and wave front singularities in the Gödel space–time

We explore wave fronts of null geodesics in the Gödel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Gödel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.