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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]

In this article, the fractional Schrödinger–Hirota equation which is a generalization of the standard Schrödinger equation which, in particular, explain how soliton transmission behaves on fiber optic systems in physics when data is transmitted over long distances with a wide bandwidth. A collection of comprehensive soliton structures are developed to study the behaviour of the governing model with the aid of some efficient explicit strategies namely the exp (- ψ (ζ)) -expansion method and the Sardar sub-equation method. By transforming the original equation into a system of ordinary differential equations, it becomes possible to obtain explicit solutions with a high degree of accuracy. These solutions incorporate dark soliton and trigonometric function solutions, dark singular solition plane wave, singular solition, opposite singular solition, smooth, bell shaped, w-shaped periodic, bright, anti kink, singular bell shaped solitons and traveling wave structures. [ABSTRACT FROM AUTHOR]

The Hamiltonian amplitude equation that describes the transmissions of wire optical technology along wave propagation in the physics linked disciplines can be solved by utilizing the unique analytical and semi-analytical approaches namely the polynomial expansion method and the Adomian decomposition technique. Various types of soliton solutions are attained that express different behaviours including singular and v-shaped soliton solutions behaviour. The developed solutions are highly important in dealings the wave behaviour in mathematical physics related fields and in the transmission of optical fibers. The approaches applied in this paper are not utilized in given model so we apply these strategies to attain the soliton solutions. Hence we conclude the the results attained are unique, robust and newly made that proves novelty of the work. Furthermore, we study the stability plus the modulation instability of the given model. The 3D, contours, and 2D graphics are visualised to demonstrate the dynamical structures of the established results more efficiently. [ABSTRACT FROM AUTHOR]

The nonlinear (4+1)-dimensional Fokas equation (FE) has been demonstrated to be the integrable extension of the Kadomtsev–Petviashvili (KP) and Davey–Stewartson (DS) equations. In nonlinear wave theory, the governing model is one of the fundamental structures that explains the surface waves and interior waves in straits or channels with different depths and widths. In this study, the generalized unified approach, the generalized projective ricatti equation technique, and the new F/G-expansion technique are applied to investigate the higher dimensional nonlinear model analytically. As a result, several solutions are successfully achieved, including dark soliton, periodic type solitons, w-shaped soliton, and single-bell shaped solitons. Along with an explanation of their behavior, we also display a few of the equation's exact solutions graphically. The results demonstrate the effectiveness and simplicity of the approaches mentioned in this article, demonstrating their applicability to a wide range of additional nonlinear evolution issues in numerous scientific and technical disciplines. [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]

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]

In this study, we solve by involving conformable fractional derivative on time-fractional perturbed nonlinear Schrödinger model which describe the behaviour of soliton transmission on fibers optical system in physics specially in transmission of data over long distances with large bandwidth. There are two modern techniques are utilized for solving the suggested model namely the Extended hyperbolic function technique and the polynomial expansion technique. These techniques give unique, robust, and powerful solutions that are useful in many research areas. We attain different types of solutions that give unique behaviour of V shaped, singular solution, and periodic soliton solutions. These solutions are play a vital role in the soliton theory along with data transmission in optical fibers. Further we also discuss the stability of obtain solutions as well as the modulation instability of the governing NLSE. To grasp and better understanding of the solution behavior we include the 3D, contour and 2D graphics. [ABSTRACT FROM AUTHOR]

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu–Eckhaus model with full non-linearity are obtained by utilizing the exp a function technique and modified extended tanh expansion function technique. The equation was independently introduced by Wiktor Eckhaus and by Anjan Kundu to model the propagation of waves in dispersive media. The model Kundu–Eckhaus equation is a general form of integrable system that is Gauge-equivalent to the mixed nonlinear Schrödinger equation. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The obtained solutions may be used for the propagation of the ultra-short femtosecond pulses and the rogue wave in an optical fiber. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day. [ABSTRACT FROM AUTHOR]

The shallow water equation, which describes fluid flow below a pressure surface, is the structure that is most frequently used for displaying free surface flows. This particular kind of approach takes into consideration the impact of gravity on fluids through the inclusion of a source term proportional to the product of the water level and ground slopes. The given model is converted into a bilinear form using the Hirota bilinear method. Which refers to the development of lump waves, collisions between lump waves and periodic waves, collisions between lump waves and single- and double-kink soliton solutions, and collisions between lump, periodic, and single- and double-kink soliton solutions. Furthermore, the exp (- ϱ (ς)) approach are applied to obtain several forms of innovative combinations for the governing dynamical fractional model. In addition, it has been confirmed that the established results are stable, and it has been helpful to validate the calculations. Moreover, multiple intriguing exact solutions are utilized to illustrate the physical nature of 3D, contour, and 2D graphs. The solution yields a set of bright, dark, periodic, rational, and elliptic function solutions. [ABSTRACT FROM AUTHOR]

In this article, the (2+1)-dimensional nonlinear hyperbolic Schrödinger model is studied analytically which specifies the proliferation of optics signal in single-mode fiber optics by using the unified technique, the exp(- δ (ζ) ) technique and the polynomial expansion technique. These techniques can give solutions of different kind that has application in physical mathematical fields, optical wave structure, and many other fields that are related to wave transmission. As compared to other approaches these used methodology are effective, unique, and easy to applicable for solving the complex models in Physics. The waveform in electromagnetic domains topics are discussed using this model as a governing equation. For a given set of pertinent parameters, the dynamics of various wave structures are visualised in 3D, 2D, and contour using Mathematica. These solutions exhibit singular periodic, multi-periodic, optical, singular and multiple bell-shaped, and μ-shaped solitons solutions as their behaviour. Further we study the stability and modulation instability (MI), also some plots are drawn for better understanding of solution. The solutions derived from the utilized techniques describe that these approches are easy, potent and uncomplicated, and these can be applicable for solving many other NLSE in Mathematical physics, and also in different field of natural sciences. The solution obtain are newly made because according to my best knowledge these methodology are not applied to this model in previous. [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]