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Studying the highly dispersive model with arbitrary refractive index initiated by Kudryashov is the subject of this work. This model depicts the behavior of soliton propagation via polarization-preserving fibers. To secure a dark soliton and like-solitons with singularities solution for the proposed model, the generalized Kudryashov's integration approach has been utilized. This method do not have any constraints on how to find solutions. Some significant solutions have been graphically elaborated in the form of 2D and 3D plots by selecting the appropriate parameters to provide a better physical illustration and understanding of the dynamical physical properties of this model. [ABSTRACT FROM AUTHOR]

The newly developed (3+1)-dimensional nonlinear Kudryashov's equation offers a framework for studying the behavior of propagating modulated envelope signals and is particularly useful in the fields, where the propagation of wave-like phenomena is essential such as in the field of fluid dynamics, it helps to analyze phenomena like water waves and fluid flow behavior. In plasma physics, it helps to understand plasma instabilities and fusion device behavior. To obtain soliton solutions for the (3+1)-dimensional nonlinear Kudryashov's equation, the ϕ 6 -model expansion method is employed to derive various forms of solitons, each with its own unique characteristics and properties. This analytical technique is known for its effectiveness in constructing soliton solutions for nonlinear equations and also provides constraints and conditions for the existence of these solitons. Furthermore, the study effectively emphasizes the physical significance of the proposed equation by presenting insightful graphical representations of the constructed soliton solutions. By considering a higher level of nonlinearity, this latest version of the equation presents a significant advancement in the understanding of soliton dynamics and provides a more comprehensive framework for studying wave phenomena. Our study delves into the fascinating realm of wave propagation and soliton dynamics, making a significant and original contribution to this field. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to reach the exact solutions of the p-forced nonlinear Klein–Gordon equation by using a novel method called the Nucci reduction method. The nonlinear Klein–Gordon equation finds applications in various real-world scenarios. One notable application is in the field of nonlinear optics, where the equation is used to study the propagation of intense laser beams through nonlinear media. Nonlinear Klein–Gordon equations are also employed in condensed matter physics to model the behavior of superconductors and superfluids. Additionally, these equations have been used in cosmology to study the dynamics of scalar fields during the early universe and their role in inflationary models. The nonlinear Klein–Gordon equation has proven to be a valuable tool in understanding and predicting the behavior of scalar fields in a wide range of physical systems. Some exact solutions with the first integrals of the proposed model have been successfully achieved utilizing the Nucci reduction technique. In order to observe the strengths of the method, three-dimensional and density graphs of the solutions are presented. [ABSTRACT FROM AUTHOR]

The study focuses on the combination of three mathematical models, namely nonlinear Schrödinger's equation, Lakshmanan–Porsezian–Daniel model, and Sasa–Satsuma model, which is called the concatenation model. The study investigates optical solitons and other exact solutions using a modified extended mapping approach. The solutions derived include bright solitons, dark solitons, combo bright-dark soliton solutions, singular solitons, periodic and singular periodic solutions, exponential and rational solutions, and Jacobi elliptic solutions. The study considers constraints on the parameters to ensure the existence of the obtained soliton solutions. Selected solutions are depicted graphically to demonstrate their physical nature. [ABSTRACT FROM AUTHOR]

This paper investigates the (2+1)-dimensional Korteweg-de Vries (KdV) equation with a local M-derivative and beta derivative in the time direction. Investigation on the (2+1)-dimensional Korteweg-de Vries (KdV) equation with a local M-derivative and beta derivative in the time direction is important because it provides insights into the behavior of nonlinear waves and has potential applications in various fields such as fluid dynamics, plasma physics, and optics. We apply Nucci's reduction method to obtain exact solutions of this equation, including solitary wave solutions, periodic wave solutions, and rational solutions. Our results demonstrate the significant effects of the M-derivative and beta derivative on the solutions, including changes in the wave speed and the introduction of additional phase constants. Finally, we discuss the physical implications of these solutions. Overall, this work highlights the importance of considering local derivatives in the study of nonlinear partial differential equations and demonstrates the effectiveness of Nucci's reduction method in obtaining exact solutions of the (2+1)-dimensional KdV equation. [ABSTRACT FROM AUTHOR]

The existence of solutions of coupled system of bi-harmonic Schrödinger equations as fixed point of an operator has been given in this article. The corresponding estimates for the length of continuity of solutions have been constructed. By applying new ϕ 6 model expansion, exact traveling wave solutions of the system have been extracted in the form of Jacobi elliptic functions. Particularly, trigonometric and hyperbolic functions can be obtained by applying the limits to Jacobi elliptic functions tending to zero or 1. The obtained solutions have been simulated and the resulting smooth waves have been plotted. [ABSTRACT FROM AUTHOR]

There are various types of fractional derivatives in literature e.g. Caputo, Riemann-Liouville, conformable and so on. In the present paper, a new integrable nonlinear Schrödinger type equation in (2+1)-dimensions is investigated, which describes the spin dynamics of Heisenberg ferromagnetic spin chains. Some bright and dark solitons and other exact solutions of this equation with conformable time fractional derivative are reported. Then, fractionalize effects of this model are graphically investigated. Moreover, the simplest equation method and Nucci’s method are utilized for differential equations with conformable fractional derivatives. [ABSTRACT FROM AUTHOR]