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This study proposed a modified G′/G2-expansion method to seek the new exact traveling wave solutions of the Newell–White–Head–Segel (NWHS) Model. This is an amplitude equation utilized for distributing temperature within a rod that is infinitely thin and long, or determining the flow velocity of a fluid through a pipe that is infinitely long but has a small diameter. The modified G′/G2-expansion method is used to extract the new exact solutions. The solutions of this model are categorized in hyperbolic, trigonometric, and rational forms. Moreover, we compare our results with the new auxiliary equation method. The 3D, line and corresponding contour representation of these solutions are depicted by choosing the different values of parameters. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is the investigation of the truncated M fractional Kuralay equation, which finds applicability in various domains such as engineering, nonlinear optics, ferromagnetic materials, signal processing, and optical fibers. As a result of its capacity to elucidate a vast array of complex physical phenomena and unveil more dynamic structures of localized wave solutions, the Kuralay equation has received considerable interest in the scientific community. To extract the solutions, the recently developed integration method, referred to as the modified generalized Riccati equation mapping (mGREM) approach, is utilized as the solving tool. Multiple types of optical solitons, including mixed, dark, singular, bright-dark, bright, complex, and combined solitons, are extracted. Furthermore, solutions that are periodic, hyperbolic, and exponential are produced. To acquire a valuable understanding of the solution dynamics, the research employs numerical simulations to examine and investigate the exact soliton solutions. Graphs in both two and three dimensions are presented. The graphical representations offer significant insights into the patterns of voltage propagation within the system. The aforementioned results make a valuable addition to the current body of knowledge and lay the groundwork for future inquiries in the domain of nonlinear sciences. The efficacy of the modified GREM method in generating a wide range of traveling wave solutions for the coupled Kuralay equation is illustrated in this study. [ABSTRACT FROM AUTHOR]

This paper is mainly concerning the study of truncated M-fractional Kuralay equations that have applications in numerous fields, including nonlinear optics, ferromagnetic materials, signal processing, engineering fields and optical fibers. Due to its ability to clarify a wide range of sophisticated physical phenomena and reveal more dynamic structures of localized wave solutions, the Kuralay equation has captured a lot of attention in the research field. The newly designed integration methods, known as the modified Sardar subequation method and enhanced modified extended tanh expansion method are used as solving tools to validate the solutions. The goal of this study is to extract several kinds of optical solitons, such as mixed, dark, singular, bright-dark, bright, complex and combined solitons. Due to the many potential applications for superfast signal routing techniques and shorter light pulses in communications, the optical propagation of soliton in optical fibers is now a topic of significant interest. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. In addition, exponential, periodic, hyperbolic solutions are generated. The applied approaches are efficient in explaining fractional nonlinear partial differential equations by providing pre-existing solutions and also producing new solutions by combining results from multiple processes. Additionally, we plot the contour, 2D, and 3D graphs with the associated parameter values to visualize the solutions. The results of this study show the effectiveness of the approaches adopted and help enhance comprehension of the nonlinear dynamical behavior of specific systems. We expect that a substantial amount of engineering model specialists will greatly benefit from our work. The findings demonstrate the efficacy, efficiency, and applicability of the computational method employed, particularly in dealing with intricate systems. [ABSTRACT FROM AUTHOR]