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The improved F-expansion method is used in this work to investigate the nonlinear Landau–Ginsberg–Higgs (NLLGH) equation. The nonlinear Landau–Ginsberg–Higgs equation mainly depicts nonlinear wave propagation, categorizes wave velocity, and materializes several phenomena via a dispersive system. New solitary wave structures are extracted by combining various solitons, such as periodic singular solitons, dark solitons, bright solitons, kink solitons, and anti-kink solitons. By using the numerical simulation, the physical analyses of solitary wave structures are visualizing graphically as 3D, contour and 2D plots. The improved F-expansion approach is a basic analytical approach for studying the movement of solitary wave structures inside the nonlinear Landau–Ginzburg–Higgs equation. Extracted solitons are important in many domains, including nonlinear optics, optical fibers, nonlinear dynamics, soliton wave theory, communicational system, ocean engineering and condensed matter physics. Because of its complicated nonlinearities, the NLLGH equation poses a severe task for kind soliton dynamics. However, the improved F-expansion method is a efficient, powerful, concise approach to unraveling these complications. [ABSTRACT FROM AUTHOR]

The primary objective of this article is to construct novel solitary wave solutions for the nonlinear (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation with a conformable derivative by employing the subsidiary ordinary differential equation method and 1 φ (ς) , φ ′ (ς) φ (ς) method. The solutions obtained encompass diverse bright, dark, singular, and periodic solitary waves. Additionally, the article thoroughly discusses the sufficient conditions for the existence of these solutions. To visually represent the obtained solutions, we include 2D and 3D graphical images using the computational software Maple 18. We also included a comparison of fractional derivatives at different values of fractional order and conducted an analysis to understand the influence of nonlinear parameters on wave behaviors. The significance of these solutions lies in their wide-ranging applications in applied sciences and mathematical physics. Furthermore, the proposed methods are invaluable in efficiently solving nonlinear partial differential equations prevalent in engineering and physical science. [ABSTRACT FROM AUTHOR]

This study explores optical solitons in the Biswas–Arshed equation within birefringent fibers. Employing the unified solver method, the 1 φ (η) , φ ′ (η) φ (η) method, and new Kudryashov's method, we extract various optical soliton solutions, encompassing dark, singular, bright, and periodic forms. These solutions deepen our understanding of dynamic phenomena in birefringent fibers, showcasing their potential practical applications. The results, effectively visualized in 3D and 2D plots, reveal intricate patterns. Our research underscores the efficacy and simplicity of these approaches in obtaining optical solitons for diverse nonlinear evolution equations. The novelty lies in the advanced methodologies applied to investigate the Biswas–Arshed equation, yielding a diverse array of soliton solutions and their practical implications. This study not only presents a variety of solutions but also highlights their applicability across disciplines and real-world scenarios. Consequently, our research significantly contributes to advancing our understanding of optical solitons in birefringent fibers, offering a methodological breakthrough in engineering and applied physics. [ABSTRACT FROM AUTHOR]

In this study, with the help of improved exp (- Φ (η)) -function method, we explored the soliton solutions for the well-known nonlinear Fisher and nonlinear diffusion dynamical equations. Both nonlinear equations are useful for studying fluid dynamics, biology population models, plasma, fiber optics and crystallization. Our obtained results are in the form of singular bright solitons, combined bright-dark solitons, singular dark solitons, kink wave solitons, and anti-kink solitons as well as the physical structure of the extracted solutions as drawn by three-dim graphically by utilizing numerical simulation. The method is applied on two different nonlinear models, which reveal the use and simplicity of the method. It has been verified that the proposed technique yields a wide range of solutions and provides a more powerful computational approach for investigate the nonlinear evolution equations in engineering and the mathematical sciences. Our extracted results are interesting, more general, some novel and will play important role in various field of science such as nonlinear optics, quantum physics, nonlinear dynamics, laser optics, fiber optics, plasma physics, soliton wave theory, communicational system and field of engineering. The extracted results demonstrated that the utilized approach is effective, powerful, and efficient for soliton results to the nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation is used to model various phenomena, such as solitons self-focusing effects and rogue waves. In the ocean engineering, the modified nonlinear Schrödinger equation investigates the behavior of water waves, considering the complex interaction of dispersion nonlinearity, and dissipation effects. By introducing fractional derivatives to the model, the M-fractional conformable modified nonlinear Schrödinger equation allows for the investigation of fractional order effects, which can study more accurately the behavior of wave propagation in real-world ocean engineering. The novelty of our research lies in the application of of the M-fractional conformable derivative on the governed equation which represents an advancement in the existing work, which have used nonlinear Schrödinger equations without fractional derivatives. Two powerful techniques: the Jacobi elliptic function method and unified solver method are applied to attain solutions to the M-fractional modified nonlinear Schrödinger equation. The several results, including dark, bright, singular, periodic, and dark-bright soliton solutions are obtained which provide valuable insights into the complex behavior of water waves in ocean engineering. Additionally, 3D and contour graphs have been provided to visually illustrate the impact of the fractional order. We also illustrate these solutions at different values of the fractional order which explain how variations in this parameter affect wave propagation. These findings will contribute to the advancement of ocean engineering techniques, enhancing our ability to design and implement effective solutions for coastal protection, offshore structures, and marine renewable energy systems. [ABSTRACT FROM AUTHOR]