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The Schrödinger–Hirota equation is one of the most important models of contemporary physics which is popular throughout the broad fields of fluid movement as well as in the study of thick-water crests, liquid science, refractive optical components and so on. In this paper, we utilize the Hirota bilinear technique and the unified technique to attain various soliton solutions of the governing model analytically. These approaches are robust, powerful and unique also have many applications in different fields of mathematical physics. The solutions attained from these techniques are highly valuable and useful in various fields of sciences specially in the transmissions of optical fibers, also they give different behaviors including V-shaped and periodic soliton solution behavior. Further, the approaches applied here are not applied in this model previously. Therefore, ours is a new work, which summarizes its novelty. The 3D, 2D and contour plots are included to grasp the understanding of solutions' behavior. These findings are valuable in electronic communications such as elliptical circuits and in investigation of solitude controlling. [ABSTRACT FROM AUTHOR]

One of the most important physical models for describing the dynamics of optical soliton propagation in the theory of optical fibers is the nonlinear Schrödinger equation (NLSE). Since there are so many uses for ultrafast signal routing systems and brief light pulses in telecommunication, optical soliton propagation in nonlinear optical fibers is a subject of intense current interest. The conventional Khater approach and the extended direct algebraic method are used in this research to study a generalized unstable space–time fractional NLS model in mathematical physics. This leads to the discovery of solutions for the bright, dark, periodic, rational and elliptic functions. To illustrate the physical nature of the nonlinear model, the contour plots in 3D, 2D and 2D are produced by assigning the appropriate values to the arbitrary constants. Additionally, consideration is given to the stability analysis of the solutions to the governing equation. In the current era of communications network technology and nonlinear optics, the applied strategy appears to be a more potent and effective way for producing precise optical solutions to a number of various modern models of recent generations. [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 most important physical structure that is assumed to illustrate the geometry of optical soliton replication in optical fiber theory is the nonlinear Schrödinger equation (NLSE). Optical soliton generation in nonlinear optical fibers is a topic of great contemporary interest because of the numerous applications of ultrafast signal routing systems and short light pulses in communications. This analysis's main goal is to create a large number of soliton solutions for the dynamical model using a variety of contemporary analytical methods. This paper studies different soliton solutions to the perturbed NLSE with Kerr law nonlinearity using two sets of two distinct integration strategies: the mapping approach and the unified auxiliary equation method. The majority of solutions have been found as Jacobi elliptic functions with limiting ellipticity modulus values. Solitons like dark, bright, optical, lonely, and others are also retrieved. We were able to create various single‐type solutions with the help of these strategies. As a result, there is a variety of optical, bell‐shaped, single periodic, and multi‐periodic solutions. In order to validate the computations, the stability of the acquired findings must also be proven. The study provides a highly stunning and suitable strategy for combining numerous exciting wave demonstrations for more advanced models of the present era. Furthermore, we can assert that the outcomes reported here are unique and novel. [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]

The generalized Korteweg–de Vries–Zakharov–Kuznetsov model is one of the dominant nonlinear complex structures to exhibit the influence of magnetic fields on weak ion‐acoustic waves in plasma made up of cool and hot electrons. In this study, the nonlinear higher dimensional model is subjected to the extended F$$ F $$‐expansion approach and the exp(−ϕ(ζ))$$ \exp \left(-\phi \left(\zeta \right)\right) $$‐expansion strategy in order to discover some novel traveling waves solutions and other exact solutions. There have been several solutions discovered, such as bright, dark, periodic, bell‐shaped, and single bell‐shaped wave structures. Furthermore, the stability analysis of the model is also reported along with the dynamical visualization of the charismatic behavior of various solitons with the aid of 3D, 2D, and contour plots. The proposed techniques can also be implemented to analyze a wide range of nonlinear evolution models emerging in diverse disciplines of science and technology including mathematical physics and plasma physics. [ABSTRACT FROM AUTHOR]

In this paper, we study the perturbed nonlinear Schrödinger equation (P-NLSE) representing the propagation of waves and may be regarded as a nonlinear complicated physical model. We use the modified extended Tan hyperbolic function (METhF) approach and the ( G ′ G 2 ) -expansion approach to construct some new traveling wave structures. Several solutions have been found including dark soliton, periodic-type solitons, bell-shaped solitons, single bell-shaped solitons. We also show a graphical representation of a number of exact solutions to the dynamical model together with a description of their behavior. The proposed techniques can also be extended to various nonlinear evolution models in mathematical physics and engineering. [ABSTRACT FROM AUTHOR]

In this study, the (2+1)-dimensional generalized Hirota–Satsuma–Ito model is studied extensively to investigate wave dynamics of shallow water. A set of state of the art analytical approaches are being employed to acquire several fascinating wave structures. We have established a comparison between exact and numerical solutions to determine the absolute error. Moreover, the modulation instability as well as the stability of the solutions are adequately discussed. The 3D, contour and 2D plots are displayed for several interesting exact solutions to understand their behaviour. These strategies are demonstrated as more strong, effective, and efficient in developing various new wave structures which have numerous applications in several mathematical physics domains. [ABSTRACT FROM AUTHOR]