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The nonlinear Schrödinger equation is one of the most important physical model in optical fiber theory for comprehension of the fluctuations of optical bullet development. In this study, the exact bullet solutions for the (3+1)-dimensional Schrödinger equation which demonstrate the bullet behaviours in optical fibers can be accumulated through the Sardar sub-equation method and the unified method. The applied strategies may retrieve several kinds of optical bullet solutions within one frameworks as well as is quite simple and reliable. Mathematica are utilised for describing the dynamics of different wave structures as 3D, 2D, and contour visualisations for a given set of parameters. As a result, we are able to develop a variety of travelling wave structures namely the periodic, singular and V shaped soliton wave solutions. The stability analysis for the derived results is analysed efficiently while the modulation instability for the governing model has also been studied to demonstrate the reliability of the research. The approaches implemented here works perfectly and can be extended to deal with many advanced models in contemporary areas of science and engineering. The solutions attain by using these techniques are robust, unique and straight forward and has applications in different fields of physics, engineering and mathematical science. Specially physical applications of these obtain results are in the transmission of data in optical fibers. We also add the graphics for the better understanding of the attain solutions behaviour. [ABSTRACT FROM AUTHOR]

The problem studied in the quadratic-cubic fractional nonlinear Schrödinger model in superfast fibers is the propagation of optical pulses in fiber optic systems. Optical pulses in fiber optic systems are important because they enable the transmission of information over long distances at high speeds with minimal loss and interference. We utilized the unified method and the extended simple equation method. These methods have been instrumental in obtaining important results in the study of the quadratic-cubic fractional nonlinear Schrödinger model in superfast fibers. These methods have allowed researchers to gain a deeper understanding of the dynamics of optical pulses and have contributed to advancements in fiber optic communication systems. Superfast fibers have revolutionized data transmission by providing high-speed and reliable connectivity. They enable faster internet connections, support emerging technologies, and have implications for various industries. While there are challenges associated with their deployment and maintenance, the benefits of superfast fibers outweigh these limitations. One of the key novelties of the this model is its ability to accurately describe the propagation of ultrafast optical pulses in highly nonlinear fibers. The model takes into account both quadratic and cubic nonlinear effects, which are known to play crucial roles in the dynamics of intense light pulses. [ABSTRACT FROM AUTHOR]

A broad spectrum of opportunities for ultrafast information processing and light pulses in communications has sparked a lot of interest in the field of wave propagation in nonlinear fibers. In this work, some new analytical soliton solutions to the perturbed nonlinear Schrödinger equation are constructed. To illustrate several soliton solutions for various parameter values, 3D simulations were carried out. Dark, bright, optical, solitary, and other solitons are also retrieved. We were able to create multiple single-type solutions using these methods. The observed results are especially intriguing since they give researchers a better computational tool for developing numerous travelling wave solutions to nonlinear equations that have recently appeared in diverse disciplines of science and engineering. A variety of optical, bell-shaped, singular, periodic, and multiple periodic solutions are produced as a result. The stability of the results is also proven in order to validate the computations. The study provides a highly spectacular and acceptable way to mix many fascinating wave displays for more complex current period models. We can also claim that the outcome we're talking about is fresh and original. [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]

In the theory of optical fibres, the nonlinear Schrödinger equation is one of the most significant physical models for understanding the dynamics of optical soliton proliferation. Optical soliton propagation in nonlinear optical fibres is a topic of considerable contemporary interest due to the wide range of applications for ultrafast signal routing systems and short light pulses in communications. Our basic objective of this investigation is to use different modern analytical techniques to develop several soliton solutions for the resonance model. As an outcome, a variety of periodic solitons and singular bell shaped solitons solutions are obtained. Furthemore, the findings of stability as well as its modulation instabilities are effectively analyzed. The adapted schemes seem very impressive and competent avenue to obtained several advanced moving pulse shapes of different coincident pattern in the recent decade. [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]