Coefficient Of Cubic Nonlinearity Research Articles

Stable high-dimensional solitons in nonlocal competing cubic-quintic nonlinear media

We find and stabilize high-dimensional dipole and quadrupole solitons in nonlocal competing cubic-quintic nonlinear media. By adjusting the propagation constant, cubic, and quintic nonlinear coefficients, the stable intervals for dipole and quadrupole solitons that are parallel to the x-axis and those after rotating 45° counterclockwise around the origin of coordinate are found. For the dipole solitons and those after rotation, their stability is controlled by the propagation constant, the coefficients of cubic and quintic nonlinearity. The stability of quadrupole solitons is controlled by the propagation constant and the coefficient of cubic nonlinearity, rather than the coefficient of quintic nonlinearity, though there is a small effect of the quintic nonlinear coefficient on the stability. Our proposal may provide a way to generate and stabilize some novel high-dimensional nonlinear modes in a nonlocal system.

Controlling Properties of Interfaces in Nonlinear Sandwich-Type Structures with a Defocusing Internal Layer

A model of a three-dimensional optical structure in which the plane-parallel boundaries have intrinsic nonlinear properties is considered. The internal layer with a finite thickness is an optically transparent medium with defocusing Kerr nonlinearity; on the outside, it is in contact with dielectric linear half-spaces. The mathematical formulation of the model reduces to the nonlinear Schrodinger equation with a positive coefficient of cubic nonlinearity and with a nonlinear self-consistent potential. It is shown analytically that the system contains a nonlinear light wave propagating along the optical layer and localized in dielectric plates. The frequencies of light-field localization in this structure are obtained and the conditions for their existence are determined for different characteristics of the media and the interfaces between them. It is shown that the light field can be localized along the layers for different signs of the nonlinear response of the interfaces between layers of the three-layer structure in the case where one of them is characterized by a focusing nonlinearity; and the other, by a defocusing one.

Compression of optical similaritons induced by cubic-quintic nonlinear media in a graded-index waveguide

We employ the similarity reductions in two steps to obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrödinger equation. Also, parameter domains are delineated in which kink and double-kink similaritons exist for this model. This methodology introduces a free parameter through cubic nonlinearity coefficient which gives us freedom to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide. Furthermore, we observe rapid beam compression of these similaritons for varying detuning parameter and the coefficient of cubic nonlinearity.

Energy harvesting of monostable Duffing oscillator under Gaussian white noise excitation

Energy harvesting of monostable Duffing oscillator with piezoelectric coupling under Gaussian white noise excitation is investigated. Based on the Fokker–Plank–Kolmogorov equation of piezoelectric coupling systems, the statistical moments of the response are derived from the Van Kampen expansion. The effects of the spectral density of the random excitation and the coefficient of cubic nonlinearity on the expected response moments are analyzed. Some numerical examples are presented to demonstrate the effects of excitation spectral density, coefficient of cubic nonlinearity and initial conditions on the output voltage.

Transition of a nonlinear internal wave through an overturning point on a shelf

It is well known that various processes of generationand transformation of a nonlinear internal wave (IW)occur on the shelves of oceans and seas [1–5]. A longIW (in most cases, of tidal origin) propagates over theshelf to the coast and usually transforms nonlinearly,leading to the generation of solitary or soliton-like IWs.In this case, one can see an interesting effect related tothe specific waveguide of IWs on the shelf, which canbe called the effect of polarity change of IW amplitude.It is known from observations that intense IWs propa-gating in the pycnocline near the sea surface attain theform of depression waves (the wave profiles havesmooth crests and sharp troughs). In contrast, IWs inthe bottom thermocline with smooth troughs and sharpcrests resemble elevation waves [1]. A specific propertyof the shelf is the fact that it can include two regions ofpossible existence of IWs of different polarities. Theseregions are divided by the so-called overturning point(in reality, it is a more or less elongated zone). This is apoint on the shelf where the pycnocline is located atequal distances from the sea surface and bottom (i.e., itis located in the middle of the water column). All IWspropagating from deeper regions to the shore necessar-ily pass this point. As this takes place, the depressionwaves are transformed to elevation waves (Fig. 1).In 1982, the effect of polarity change in the IWamplitude was observed for the first time in Russianwaters on the shelf of the Sea of Japan [1, 6]. A fewyears later, similar observations were carried out in theEast Mediterranean [7]. New interesting data on theobservation of this effect were recently obtained in theSouth China Sea [8]. Progress was gained in modelingof the process discussed here. Numerical modeling ofthe modified Korteweg de Vries equation (or Gardnerequation) allows us to find some peculiarities of thetransformation of solitary negative waves to positivewaves for the case of two-layer stratification describedin [9]. At the overturning point, the coefficient of qua-dratic nonlinearity α turns to zero. However, the coeffi-cient of cubic nonlinearity starts to play its role, whichcan be either positive or negative depending on theform of density stratification. The influence of the signof cubic nonlinearity on the transformation of a longIW in the overturning region was studied in [10].Our work shows field data compared with detailednumerical modeling and includes two interrelatedstages. At the first stage, we present the results of rareobservations of an intense IW that passes the overturn-ing point obtained in our observations in the summerseason on the Pacific shelf of Kamchatka. At the secondstage, we studied the entire process of the transforma-tion of an IW of negative polarity to a wave of positivepolarity using numerical modeling. Actually measuredparameters of the observed IW and the medium of itstransition were used as the model parameters.OBSERVATION DATADuring the investigations on the Pacific shelf ofKamchatka in the summertime (the observations werecarried out in August 1990), we recorded several inter-esting examples of intense IWs propagating in the ther-mocline located close to the middle of the water col-umn. The measurements were made from a shipanchored at a depth of 33 m at a distance of 1 km fromthe coast. The ship was equipped with a spatial antennaof three 20-m-long line temperature sensors (LTS)located at the corners of triangle with sides equal to 25,27, and 46 m. Each LTS placed vertically covered thetemperature interface layer within levels from 7 to 27 m.Such an antenna allows us to measure the direction ofIW transition, wavelength, and velocity of its transition[11, 12]. We also used a CTD profiler for obtaininginformation about the location of the pycnocline. Insome cases, we operated in the continuous profiling

Noise shear waves in nonlinear smectic liquid crystal

The propagation of a narrow-band shear wave in a smectic liquid crystal is studied. It is shown that the nonlinearity makes possible a random phase modulation. The temporal correlation function, the characteristic correlation time, and the width of the spectrum are calculated. The relation between the width of the spectrum, the intensity of the wave, and the distance traversed is determined. This makes it possible to determine the coefficient of cubic nonlinearity of a smectic liquid crystal (SLC) by measuring the relative increase of the width of the spectrum at an arbitrary point.