Narrow Results

This study uses the modified Sardar sub-equation method to find novel soliton solutions to the nonlinear three-component coupled nonlinear Schrödinger equation (NLSE), which is used for pulse propagation in nonlinear optical fibers. Multi-component NLSE equations are widely used because they can represent a wide range of complex observable systems and more dynamic patterns of localized wave solutions. The optical solutions proposed in this study are novel and can be described using hyperbolic, trigonometric, and exponential functions. These solutions are categorized as bright, dark, singular, combo bright-singular, and periodic solutions. Some solutions’ dynamic behaviors are demonstrated by selecting appropriate physical parameter values. The results and computational analysis indicate that the techniques provided are simple, effective, and adaptable. They can be applied to a variety of nonlinear evolution equations, whether stable or unstable, and can be used in fields such as mathematics, mathematical physics, and applied sciences.

By using the generalized exponential rational function method, we construct the analytical solutions of the mitigating internet bottleneck with quadratic-cubic nonlinearity involving the $\beta$-derivative. This equation is described to control internet traffic. A number of new optical soliton solution for them are calculated. Oblique optical solutions also emerge as a product of this integration scheme. The results are applicable to mitigate Internet bottleneck, which is a growing problem in the telecommunications industry.

In this paper, the full nonlinearity form of the space–time fractional Fokas–Lenells equation is scrutinized to get new analytical solutions. To achieve this, a convenient method is applied namely, a new Kudryashov method. The achieved solutions show pulse propagation in different wave patterns such as singular bell shape, peakon, singular anti-bell shape, dark, anti-bell and bright solutions. These physical characteristics are studied thoroughly by the graphical representation, which shows the fruitfulness and functionality of the proposed method.

This paper considers the generalized nonlinear Schrödinger (GNLS) equation with group velocity dispersion and second-order spatio-temporal dispersion coefficients. We obtain new dispersive solutions of a variety of GNLS equations via the exponential rational function method with the local M-derivative of order $\alpha$. The results obtained demonstrate that the employed method is simple and quite efficient for constructing exact solutions for other nonlinear equations arising in mathematical physics and nonlinear optics.

In this paper, the generalized exponential rational function method is applied to obtain analytical solutions for the nonlinear Radhakrishnan–Kundu–Lakshmanan equation. We obtain novel soliton, traveling waves and kink-type solutions with complex structures. We also present the two- and three-dimensional shapes for the real and imaginary part of the solutions obtained. It is illustrated that generalized exponential rational function method (GERFM) is simple and efficient method to reach the various type of the soliton solutions.

This work deals with finding new complex solitons to the perturbed nonlinear Schrödinger model with the help of an analytical method. Using several computation programs, we gain entirely new solitons to the considering model. Under the choice of suitable values of the parameters, density graphs to the reported solutions, such as complex, hyperbolic, trigonometric and exponential, are successfully presented. Simulations in various dimensions are also plotted by using package programs.

In this paper, we address various optical soliton solutions and demonstrate the different dynamics of solitary waves to a (3+1)-dimensional nonlinear Schrödinger equation (NLSE) with parabolic law (NLSE) using a newly created powerful and effective method named as the extended generalized Riccati equation mapping method. This technique presents an organized manner to reveal the essential dynamics. There is great significance of the nonlinear Schrödinger equations and their several formulations in numerous fields of science, particularly in nonlinear optics, optical fibers, quantum electronics, and plasma physics. Through the use of numerical simulations and mathematical analysis, we explore the characteristics and behavior of these solitary wave solutions in a variety of scientific contexts. These results demonstrate the essential complexity of the governing equation and yield novel derived solutions. These solutions contribute to a better understanding of nonlinear wave phenomena by highlighting the fundamental dynamics establishing solitary waves in the NLSE. To enhance our wider knowledge, we provide effective graphic representations of the nonlinear wave structures in the derived solutions utilizing a variety of graphs, including 3D, 2D, and density plots. Moreover, a specific transformation has been applied to transform the system into a planar dynamical system, and several phase portraits have been presented to examine its behavior. Furthermore, upon introducing a perturbed term, chaotic behavior has been observed across different parameter values through both two-dimensional and three-dimensional graphics.

This paper deals with the investigation of the newly obtained solitary solutions of perturbed optical metamaterial with Kerr law nonlinearity. Two novel analytical techniques, namely, the extended Riccati equation rational expansion (ERERE) method and the extended rational $exp(-(\frac{{\phi }^{\prime }}{\phi })(\xi ))$-expansion (EREE) methods are applied to develop new solitary solutions. The resultant wave solutions are periodic wave solution, singular kink, anti-peakon, dark, singular anti-kink, anti-kink, gray and singular soliton solutions. The detailed dynamics of the retrieved solutions are the most potent influence of the proposed methods which shows the efficacy and fruitfulness of both the methods.

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