Search

Fractional order models involving nonlinearity are remarkable for having substantial application in real-world. The present determination is due to obtain applicable wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise. Enhanced rational (G ′ / G) -expansion and improved auxiliary equation approaches are imposed to the suggested model which accumulate diverse wave solutions in appropriate form. The investigators might depict sophisticated tangible phenomena in a wide range with the assistance of the found well-furnished wave solutions as the governing equation makes understanding about the plasma physics, the wave of propulsion fluid-flow, and the dynamic characteristics of shallow-water waves. Various obtained solutions are figured out to portray prominent physical characteristics of nonlinear wave outlines. Different types of solitons are organized graphically in 3D shapes such as periodic, anti-periodic, compacton, anti-compacton, bell, anti-bell, peakon, kink, anti-kink, cuspon etc. Diverse 2D plots are comprised to make noticeable the wave velocity while contour plots signify the association among the concerned variables. The graphical representations are brought out together with the effects of noise strength and Brownian motion. The observation of the current whole work might captivate the researchers for future related work by employing the recommended approaches which are competent, pioneering, and concise. [ABSTRACT FROM AUTHOR]

We perform a meticulous analysis of profiles of third-order nonlinear optical susceptibility (TONOS) of impurity doped quantum dots (QDs) in the presence and absence of noise. We have invoked Gaussian white noise in the present study and noise has been introduced to the system additively and multiplicatively. The QD is doped with a Gaussian impurity. A magnetic field applied perpendicularly serves as a confinement source and the doped system has been exposed to a static external electric field. The TONOS profiles have been monitored against a continuous variation of incident photon energy when several important parameters such as electric field strength, magnetic field strength, confinement energy, dopant location, Al concentration, dopant potential, relaxation time, anisotropy, and noise strength assume different values. Moreover, the influence of mode of introduction of noise (additive/multiplicative) on the TONOS profiles has also been addressed. The said profiles are found to be consisting of interesting observations such as shift of TONOS peak position and maximization/minimization of TONOS peak intensity . The presence of noise alters the features of TONOS profiles and sometimes enhances the TONOS peak intensity from that of noise-free state. Furthermore, the mode of application of noise also often tailors the TONOS profiles in diverse fashions. The observations accentuate the possibility of tuning the TONOS of doped QD systems in the presence of noise. [ABSTRACT FROM AUTHOR]

We make an extensive investigation of linear, third-order nonlinear, and total optical absorption coefficients (ACs) of impurity doped quantum dots (QDs) in presence and absence of noise. The noise invoked in the present study is a Gaussian white noise. The quantum dot is doped with repulsive Gaussian impurity. Noise has been introduced to the system additively and multiplicatively. A perpendicular magnetic field acts as a source of confinement and a static external electric field has been applied. The AC profiles have been studied as a function of incident photon energy when several important parameters such as optical intensity, electric field strength, magnetic field strength, confinement energy, dopant location, relaxation time, Al concentration, dopant potential, and noise strength take on different values. In addition, the role of mode of application of noise (additive/multiplicative) on the AC profiles has also been analyzed meticulously. The AC profiles often consist of a number of interesting observations such as one photon resonance enhancement , shift of AC peak position , variation of AC peak intensity , and bleaching of AC peak . However, presence of noise alters the features of AC profiles and leads to some interesting manifestations. Multiplicative noise brings about more complexity in the AC profiles than its additive counterpart. The observations indeed illuminate several useful aspects in the study of linear and nonlinear optical properties of doped QD systems, specially in presence of noise. The findings are expected to be quite relevant from a technological perspective. [ABSTRACT FROM AUTHOR]

We make an extensive investigation of total optical absorption coefficient (TOAC) of impurity doped quantum dots (QDs) in presence and absence of Gaussian white noise. The TOAC profiles have been monitored against incident photon energy with special emphasis on the roles played by the electric field, magnetic field, and the dot confinement potential. Presence of impurity also influences the TOAC profile. In general, presence of noise causes enhancement of TOAC over that of noise-free condition. However, the interplay between the noise and the quantities like electric field, magnetic field, confinement potential and impurity potential bring about rich subtleties in the TOAC profiles. The said subtleties are often manifested by the alterations in TOAC peak intensity, extent of TOAC peak bleaching, and value of saturation intensity. The findings reveal some technologically relevant aspects of TOAC for the doped QD systems, specially in presence of noise. [ABSTRACT FROM AUTHOR]

We make a rigorous analysis of profiles of oscillator strength of a doped quantum dot in the presence and absence of noise. The noise employed here is a Gaussian white noise. The quantum dot is doped with repulsive Gaussian impurity. Noise has been administered additively and multiplicatively to the system. A perpendicular magnetic field is also present and a static external electric field has been applied. Profile of OS has been minutely monitored with variation of several important quantities such as confinement energy, electric field strength, dopant location, magnetic field strength, dopant potential, noise strength, Al concentration, and mode of application of noise. The profiles are enriched with significant subtleties and often reveal enhancement and maximization of oscillator strength in the presence of noise. These observations are indeed useful in the study of linear and nonlinear optical properties of doped QD systems which bear sufficient technological importance. [ABSTRACT FROM AUTHOR]

This study has been carried out to examine the stochastic optical soliton solutions of the nonlinear Schrödinger's equation (NLSE) with Kerr law nonlinearity by multiplicative noise in Itô sense and the behavioral changes on soliton dynamics. In order to see the noise effect better, bright and dark soliton shapes belonging to the NLSE have been obtained using the subversion of the new extended auxiliary equation method (SAEM246) and verified with the computer algorithm that developed for this study. For the NLSE, the distortion of the soliton solutions obtained by the SAEM246 method under different noise effects is clearly shown and simulated. This method has never been applied before to a NLSE containing a stochastic function to analyze the noise effect. The novelty of the problem and applied method has resulted in many new and original soliton solutions and their behaviors under the noise effects. [ABSTRACT FROM AUTHOR]

Highlights: [•] Linear polarizability of quantum dot has been studied. [•] Quantum dot is doped with a repulsive impurity. [•] The polarizabilities are frequency-dependent. [•] Influence of Gaussian white noise has been monitored. [•] Noise exploited is of additive and multiplicative nature. [Copyright &y& Elsevier]