Search

In this study, the space-time fractional generalised reaction duffing model is investigated analytically, which is a generalization for a collection of prominent fractional models describing various key phenomenon in science and engineering. The governing equation is converted to a nonlinear ODE by the compatible travelling wave transform. The investigation established that for analysing nonlinear evolution equations of fractional order, the recommended approach is more effective and realistic. The findings are given extensively in rational forms of trigonometric function series or clearly in powers of specific trigonometric functions. A collection of bright, dark, periodic, and optical solitons is discovered. Mathematica is used to flourish the presence of some obtained solutions in 3D graphs with different fractional orders. The results show that the recommended methods are more practical and effective ways to illustrate the dynamics of several complex wave structures in modern science and technology. [ABSTRACT FROM AUTHOR]

In this paper, the new generalized stochastic fractional potential-KdV model is investigated analytically which describes the nonlinear optical solitons and photons propagating in electric circuits and multicomponent plasmas. The governing model is transformed into a bilinear form using the Hirota bilinear method. A variety of novel waves structures are developed in the form of lump waves, collisions between lump waves and periodic waves, collisions between lump waves or single and double-kink soliton solutions, collisions between lump, periodic, single and double-kink soliton solutions. Furthermore, the ( G ′ / G 2 ) expansion method and the Adomian decomposition method are employed to construct a number of new configurations for the governing dynamical model. To validate the scientific computations, a comparison study and stability analysis are carried out efficiently. Finally, to understand the dynamical behaviour of the the nonlinear fractional model, the 3D, 2D, and contour plots have also been demonstrated with the appropriate set of parameters. Depending upon the efficiency and the validity of the applied techniques, it is established that these strategies can also be applicable to many contemporary models. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE), one of the most fundamental physical models for understanding the fluctuations of optical soliton development, plays a significant role to demonstrate the dynamics of optical fibers. Therefore, the wave propagation in nonlinear dispersive medium is a subject of considerable interest due to the wide range of possibilities for ultrafast data processing and light pulses in communications. In this article, the coupled space-time fractional NLSE is investigated which is used to describe the non-relativistic quantum mechanical behaviour. A collection of comprehensive soliton structures are developed to study the dynamics of the governing model with the aid of some efficient analytical strategies. These solutions incorporate dark soliton and trigonometric function solutions, singular solition, dark singular solition plane wave, singular solition, opposite singular solition, smooth, bell shaped, periodic, bright, anti kink, singular bell and traveling wave with darkness. The presence of some attained solutions are flourish in 3D graphs with various fractional orders by using Mathematica. The results which we obtained reveal that the suggested approaches are more convenient and productive techniques to depict the dynamics of numerous complex wave structure in contemporary areas of science and technology. [ABSTRACT FROM AUTHOR]

In optical fiber theory, the nonlinear Schrödinger equation (NLSE) is one of the most important physical models for describing the transmission of optical soliton growth. Due to the large range of possibilities for superfast signal processing and light pulses in communications, the wave propagation in nonlinear fibers is currently a topic of substantial curiosity. In this study, the third order generalized NLSE is investigated analytically by using the extended hyperbolic function technique, the improved F-expansion method, and the Adomian decomposition method, which has great importance in applied physics especially in the study optical fibers. The obtained solutions are newly made also they have the form of optical solitons, singular bell shaped, multi-bell shaped, and singular periodic solitons wave behavior and have applications in the optical fibers transmission, physics and many other scientific fields. The stability along with the modulation instability (MI) of the governing model has also been examined to validate the results. The nonlinear model properties have been illustrated using 3D, 2D, and contour plots with the appropriate set of parameters, which is demonstrated to visualize the physical structures more productively. Finally, it is concluded that similar strategies can also be implemented to study many contemporary models. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation (NLSE) is one of the most important physical model in optical fiber theory for explaining changes in optical soliton growth. Due to the large range of opportunities for ultrafast signal routing systems and brief pulses of light in communications, optical soliton transmission in nonlinear fibers is currently a topic of significant interest for researchers. In this article, we study the dynamics of the generalised unstable NLSE which specified the time evolution of perturbations in barely steady or unstable media. A set of efficient analytical approaches are implemented to develop various interesting travelling wave structures such as bright, dark, singular, optical, bell shaped and periodic solitons solutions. Additionally, the stability of the obtained results is validated. Finally, the modulation instability of the governing model has also been investigated to present change effects that occurs as a result of the irregular refractive indices in an optical fiber, leading to distinct behaviour patterns. The methods as reported are applicable in clarity, effectiveness, and simplicity, establishing their applicability to various sets of dynamic and static nonlinear equations concerning evolutionary phenomena in computational physics, as well as other practical domains and numerous areas of research. [ABSTRACT FROM AUTHOR]

The purpose of this study is to employ the Sine–Cosine expansion approach to produce some new sort of soliton solutions for the cubic–quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward scattering effects that are overlooked in the more popular nonlinear Schrödinger equation. As a result, a number of novel traveling wave structures have been discovered. We also investigate the stability of solitary wave solutions for the governing model. Furthermore, the modulation instability is discussed by employing the standard linear-stability analysis. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behaviour. [ABSTRACT FROM AUTHOR]

In this work, the Lakshmanan-Porsezian-Daniel model is investigated which is the generalization of the non-linear Schrödinger model, to describes the dynamical behavior of optical solitons. The extended modified auxiliary equation mapping method is employed to develop some new exact solitary wave solutions to the complex model with the ker law, the parabolic law and the anti-cubic law nonlinearities. As a result, dark solitons, light solitons, singular solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions are established. In the current era of communications network technology and nonlinear optics, the applied strategy appears to be a more powerful and efficient approach for achieving exact optical solutions to a number of diversified contemporary models. [ABSTRACT FROM AUTHOR]

In this article, the modified Khater method is utilized to extract new analytical solutions to the cubic-quintic nonlinear non-paraxial pulse propagation model in a planar waveguide with Kerr nonlinearity, fifth-order nonlinearity, and spatiality dispersion due to non-paraxial effects. As a result, a variety of some new exact solutions are observed. Moreover, the three-dimensional shapes are visualized with the aid of the latest scientific tools. [ABSTRACT FROM AUTHOR]

The focus of this article is to find some new exact solutions to the M-fractional paraxial nonlinear Schrödinger equation with Kerr media by employing the modified simple equation method and the auxiliary equation method. A set of novel travelling wave solutions are observed such as bright, dark, periodic and optical solitons. Moreover, the physical interpretation of nonlinear waves would also be demonstrated with the aid of scientific computing. [ABSTRACT FROM AUTHOR]

In this study, a state-of-the-art approach tilted as the extended modified auxiliary equation mapping method is employed to observe some novel exact solutions to the generalized (1 + 1)-dimensional unstable space–time fractional nonlinear Schrödinger model. A variety of solitons are discovered namely, bright, dark, singular, combo, optical, singular optical and combo solitons in an elegant scheme. The existence conditions are also presented by choosing appropriate parameters to visualize the physical interpretation of solitons in three-dimensions with the aid of the latest computational tools. [ABSTRACT FROM AUTHOR]