Optical solitons in $$$$-dimensions under anti-cubic law of nonlinearity by analytical methods

The present study emphasis to look for new closed form exact solitary wave solutions for the \((n+1)\)-dimensional nonlinear Schrödinger equation using the extended trial equation method (ETEM) and the \(\exp (-\Omega (\eta ))\)-expansion method (EEM) with the help of symbolic computation package maple. As a consequence, the ETEM and EEM are successfully employed and acquired some new exact solitary wave solutions in terms of exponential based functions, hyperbolic based functions, trigonometric based functions and rational based functions. All solutions have been verified back into its corresponding equation with the aid of maple package program. Finally, we believe that the executed method is robust and efficient than other methods and the obtained solutions in this paper can help us to understand the variation of solitary waves in the field of nonlinear optic.     

Optical solitons in fiber Bragg gratings with generalized anti-cubic nonlinearity by extended auxiliary equation

This work retrieves optical solitons having generalized anti-cubic nonlinearity in fiber Bragg gratings by implementing extended auxiliary equation method. The spectrum of solitons are enumerated along with their existence criteria.     

Exact optical solitons in metamaterials with anti-cubic law of nonlinearity by Lie group method

Optical and Quantum Electronics - The graphene oxide (GO) sheets were prepared from Hummer’s method. The reduced process is important to graphene related materials for widely functional use...     

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental, multi-peak, and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Two opposite soliton self-bending signals are considered for different families of solitons. Power thresholdless fundamental and multi-peaked solitons are stable in the low power region. The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals. When solitons tend to self-bend toward the waveguide lattice, stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region. Three-peaked twisted solitons are stable in the lower (upper) cutoff region for a shallow (deep) lattice depth. Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.     

Optical solitons in 1+2 dimensions with non-Kerr law nonlinearity

The combination of grazing-incidence small-angle x-ray scattering (GISAXS)with tomographic methods and phase retrieval is proposed for thereconstruction of the three-dimensional (3D) electron density of nanometersized objects. In this approach GISAXS data from a small object arecollected successively at different azimuthal angular positions. This 3Dintensity distribution in reciprocal space is used for the phase retrievaland reconstruction of the 3D electron density. The power of our approach isdemonstrated in a series of calculations performed in the frame ofkinematical and distorted-wave Born approximation (DWBA) theories for thecase of GISAXS scattering on a 200?nm island in the form of truncatedpyramid.     

Optical solitons perturbation of Fokas-Lenells equation with full nonlinearity and dual dispersion

This paper retrieves dark, rational, periodic and combo soliton solutions that stem from Fokas-Lenells equation which is studied with full nonlinearity. These solitons appear with constraint conditions on their parameters and they are also presented. Two strategic schemes have made this retrieval successful.     

Optical solitons in medium with parabolic law nonlinearity and higher order dispersion

The nonlinear Schrödinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically. The perturbations that are third-order dispersion, fourth-order dispersion, and self-steepening are taken into account. The Ricatti equation expansion approach and Ansatz method are applied. Finally, Bright, dark as well as singular solitons are constructed under some constraint conditions.     

Optical bistability and spatial resonator solitons based on exciton-polariton nonlinearity

We show experimentally optical bistability and the existence of bright and dark resonator solitons in the strong coupling regime between quantum-well excitons and the optical field in a semiconductor microcavity. The strong coupling results in a quasi-particle exciton-polariton, which gives access to positive and negative reactive and dissipative optical nonlinearities, as opposed to the usual room temperature semiconductor nonlinearities possessing essentially only one sign. The existence range and the properties of solitons can be varied widely by the detuning between polariton states and light frequency.     

Optical spatial solitons supported by photoisomerization nonlinearity in a polymer

We present a theory for a new type of optical spatial soliton that is based on the angle hole burning mechanism of photoisomerization in some polymers. We predict that the photoisomerization nonlinearity can support steady-state dark and bright spatial solitons in the polymer. We also discuss the dependence of the FWHM of the spatial soliton on wavelengths of the background beams and on the ratio of the intensity of the background beam to that of the signal beam.     

Generation of stable multi-vortex clusters in a dissipative medium with anti-cubic nonlinearity

We demonstrate the generation of vortex solitons in a model of dissipative optical media with the singular anti-cubic (AC) nonlinearity, by launching a vorticity-carrying Gaussian input into the medium modeled by the cubic-quintic complex Ginzburg-Landau equation. The effect of the AC term on the beam propagation is investigated in detail. An analytical result is produced for the asymptotic form of fundamental and vortical solitons at the point of $r\to 0$, which is imposed by the AC term. Numerical simulations identify parameter domains that maintain stable dissipative solitons in the form of vortex clusters. The number of vortices in the clusters is equal to the vorticity embedded in the Gaussian input.     

Averaging for solitons with nonlinearity management

We develop an averaging method for solitons of the nonlinear Schr?dinger equation with a periodically varying nonlinearity coefficient, which is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations.     

Optical solitons with Kudryashov's model by a range of integration norms

This paper recovers optical solitons for the newly proposed Kudryashov’s equation which governs soliton pulse propagation through optical fibers and photonic crystal fibers. A spectrum of soliton solutions are obtained from a wide range of integration norms. The existence criteria for such solitons are enlisted. Finally, couple of numerical simulations make the paper rounded.     

Thirring optical solitons with Kerr law nonlinearity

The dynamics of Thirring solitons in birefringent fibers with Kerr law nonlinearity is addressed in this paper. An exact 1-soliton solution is obtained. Bright, dark and singular soliton solutions are described.     

Collision of optical solitons with Kerr law nonlinearity

The intra-channel collision of optical solitons, with Kerr law nonlinearity, is studied by the aid of quasi-particle theory. The perturbation terms considered in this paper are all of Hamiltonian type. It is shown that the soliton–soliton interaction can be suppressed in the presence of these perturbations, namely, the self-steepening, the third-order dispersion, the fourth-order dispersion and the frequency separation between the soliton carrier and the gain-center frequency. The prediction of quasi-particle theory are fully confirmed by direct numerical simulations.     

The solitons in Bessel lattice potential with nonlocal nonlinearity

The existence and stability of fundamental and multipole solitons in Bessel potential are studied, including linear case, and nonlocal nonlinearity cases. For linear case, the eigenvalues and eigenfunction for different modulated depths of Bessel potential are obtained numerically. For nonlocal nonlinear cases, the existence and stability of fundamental and multipole solitons are studied. The results show that there exists a critical propagation constant b _c of solitons, below which the solitons vanish. The value of b _c is associated with the eigenvalue for linear case. It is found that nonlocality can expand the stability region of solitons. Fundamental and dipole solitons are stable in the whole region and the stable range of multipole solitons increase with increasing of the nonlocal degree.     

Surface defect gap solitons in superlattices with self-defocusing nonlinearity

We put forward the existence and stability of defect surface gap solitons at the interface between uniform media and an superlattice with self-defocusing nonlinearity. We reveal that the defect plays the significant role in controlling the region of solitons existing. Various solitons are found to be existed in different gaps for different defects. For positive defects, fundamental solitons can exist stably in the semi-infinite gap, and dipole solitons can exist stably in the first gap but they are unstable in the second gap. For zero or negative defects, fundamental and dipole solitons can exist stably in the first gap and the second gap, respectively.     

Accumulation of embedded solitons in systems with quadratic nonlinearity

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multiwave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter epsilon, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of Wentzel-Kramers-Brillouin type yields an asymptotic formula for the distribution of discrete values of epsilon at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -65, and a fairly good approximation for the numerical factor in front of the scaling term.     

Propagation of solitons in thermal media with periodic nonlinearity

We address the existence and properties of solitons in layered thermal media made of alternating focusing and defocusing layers. Such structures support robust bright solitons even if the averaged nonlinearity is defocusing. We show that nonoscillating solitons may form in any of the focusing domains, even in those located close to the sample edge, in contrast to uniform thermal media, where light beams always oscillate when not launched exactly on the sample center. Stable multipole solitons may include more than four spots in layered media.     

Optical solitons and optical rogons of generalized resonant dispersive nonlinear Schrödinger's equation with power law nonlinearity

This paper obtains solitons and singular periodic solutions to the generalized resonant dispersive nonlinear Schrödinger’ equation with power law nonlinearity. There are several integration tools that are adopted to extract these solutions. They are simplest equation method, functional variable method, sine–cosine function method, tanh function method and the G′/G-expansion method. These integration techniques reveal bright and singular solitons as well as the corresponding singular periodic solutions to the nonlinear evolution equation. These solitons solutions are important in the nonlinear fiber optics community as well as in the study of rogue waves.