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In this work, we investigate the (2+1)-dimensional nonlinear electrical transmission line model (NETLM) and propose a modified generalized Riccati equation mapping (mGREM) approach for obtaining analytical soliton solutions. The NETLM characterizes wave distributions on network lines. We introduce the mGREM technique, which involves a traveling wave transformation to convert the equation into nonlinear ordinary differential equations. By applying this method, we extract various soliton solutions, including traveling waves, kink-type solitons, bell-shape solitons, and multi-solitons. These findings contribute to understanding the (2+1)-dimensional NETLM and provide valuable insights into wave distributions on network lines. To gain a comprehensive understanding of the solutions' dynamics, we conduct numerical simulations and present two-dimensional, three-dimensional, and contour graphs. These graphical illustrations offer valuable insights into voltage propagation patterns within the system. Our results contribute to the existing literature and open avenues for further investigations in the field of NETLM. The significance of this work lies in the successful application of the mGREM method to obtain diverse traveling wave solutions for the (2+1)-dimensional NETLM. By employing symbolic computation in Mathematica, we extract analytical soliton solutions, which go beyond previous efforts in the literature. The proposed approach provides a novel perspective on the NETLM equation and its soliton solutions. The obtained results enhance our understanding of the system's behavior and pave the way for future research in this domain. [ABSTRACT FROM AUTHOR]

The behavior of optical soliton solutions in optical fiber theory is described by the Schrödinger–Hirota equation, a nonlinear partial differential equation with multiple applications in science and engineering. In this work, a highly effective approach for solving the Schrödinger–Hirota equation is utilized based on the modified generalized Riccati equation mapping approach. The remarkable achievement of obtaining over one hundred plus newly-formed distinct analytical soliton solutions for the governing Schrödinger–Hirota equation is accomplished through the employment of this technique. The technique employed is characterized by its power, simplicity, and adaptiveness, enabling the extraction of various forms of soliton solutions into a unified framework. As a consequence of the applications, traveling waves, bell-shaped solitons, kink waves, and combo-multisoliton wave profiles are generated. To provide valuable insights into the behavior and characteristics of the solutions, two-dimensional, three-dimensional, and corresponding contour graphs are plotted for selected solutions. These findings contribute to the improvement of theoretical knowledge regarding the Schrödinger–Hirota equation and lay the groundwork for practical implementations. The abundant soliton solutions discovered through this method have the potential to find utility in a variety of fields, including electronics, quantum physics, and optical fibers. [ABSTRACT FROM AUTHOR]

In this work, we proposed a new modified generalized Riccati equation mapping approach to successfully extract several analytical soliton solutions for the (2+1)-dimensional nonlinear Schrödinger (NLS) equation with the help of symbolic computation works in Mathematica.The (2+1)-dimensional NLS equation is used in many fields, including plasma physics, nonlinear optics, and quantum electrodynamics. The main objective of the present work is to develop an effective methodology for solving highly nonlinear evolution equations that are influenced by the enhancement of a previously known method. The approach under consideration is a newly improved version of the classic generalized Riccati equation mapping. By taking advantage of this newly proposed method, we produced a wide range of closed-form solutions, including new optical solitons, traveling waves, and soliton-like solutions, all of which are crucial for nonlinear optics, optical fibers, and the physical propagation of electromagnetic waves. One may clearly argue that the novel method is highly effective and successful in finding exact solutions to nonlinear evolution equations. Moreover, we obtained a variety of new families of soliton-like wave solutions. By using the mathematical software Mathematica, we also created 2D, 3D, and contour graphics for some of the reported solutions by choosing suitable parameter values. [ABSTRACT FROM AUTHOR]

In this work, we use the generalized Riccati equation mapping method (GREMM) to seek solitary and periodic wave solutions to the generalized complex coupled Schrödinger–Boussinesq equations, which is a more useful model for describing the stationary propagation of coupled nonlinear upper-hybrid and magnetosonic waves in magnetized plasma. The GREMM approach is applied to compute a variety of soliton and other solutions in distinctive forms such as trigonometric, hyperbolic, singular, and interaction solutions in addition to rational. The main feature of this work is the achieved soliton solutions, which were not before constructed and are more general. All of the obtained solutions are validated by re-inserting them into the governing system with the help of mathematica. Moreover, 3D and 2D combined line profiles, as well as their contour graphics, are plotted to depict the dynamical behaviors of the retrieved solutions using numerical simulations. We exhibit how the wave profiles are impacted with varying time. Computational results demonstrate that applied research methodology and analytical results enrich the dynamics of the governing model. [ABSTRACT FROM AUTHOR]

In this work, we use two extremely efficient methods, generalized Kudryashov (GK) and generalized Riccati equation mapping (GREM), to extract various optical wave soliton solutions to the (2+1)-dimensional Davey-Stewartson Fokas (DS-Fokas) system, which is an ideal model for nonlinear pulse propagation in monomode optical fibers. The employed methods are very efficient and robust mathematical approaches for solving various nonlinear models of a variety of nonlinear Schrödinger's equations (NLSEs) in mathematical physics and sciences. Firstly, the traveling wave transformation converts the given nonlinear equation with a partial derivative into an ordinary differential equation (ODE). Then, different novel types of optical soliton solutions are attained using the abovementioned methods. Indeed, the obtained solutions are beneficial and important for explaining the physical phenomena of the DS-Fokas model. In the literature survey, we have found that these acquired solutions are very new and have not been discussed earlier. Some numerical simulations of the solutions have been performed for a better understanding of the results obtained with the use of symbolic computations. Furthermore, these obtained solutions are discussed graphically to attain a deep knowledge and vision of the mechanisms of all nonlinear phenomena. As a result, the wave profiles of the lump soliton, bell-shaped soliton, anti-bell-shaped soliton, periodic soliton, multisoliton, and other solitons have been displayed using three-dimensional (3D) contour plots and two-dimensional (2D) plots created with the computer software Mathematica 11.3. Moreover, the above-utilized techniques have been assumed to be essential tools for describing some nonlinear physical phenomena, namely, the nonlinear pulse propagations in monomode optical fibers, fluid mechanics, and plasma physics. [ABSTRACT FROM AUTHOR]