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This study purposes to extract some fractional analytical solutions of the Peyrard-Bishop-Deoxyribo-Nucleic-Acid (β -PBDNA) dynamic model with the beta-derivative by the unified Riccati equation expansion method (UREEM). Furthermore, we examine the role of various parameters of the fractional model on the soliton dynamic. The research focuses on computational biophysics and materials science, examining the impact of various parameters on the fractional model. This paper contributes to understanding soliton solutions and the β -PBDNA dynamic model, demonstrating the applicability of the UREEM method to various fractional models. Some soliton solutions of the model are successfully generated by applying the UREEM. Implementing the UREEM, we take a fractional wave transformation to convert the model into a nonlinear ordinary differential equation. So, a linear equation system is generated. After the system is solved, the soliton solutions are gained for the appropriate solution sets. Finally, 3D, 2D and contour graphs of diverse solutions are depicted at suitable values of parameters. In addition, this paper presents 3D, 2D and contour graphs of various solutions with suitable parameter values. The results are beneficial for interpreting the model in future work and confirm that UREEM is effectively applicable to diverse fractional models, coupled with a comprehensive graphical analysis of how different parameters influence these solutions. [ABSTRACT FROM AUTHOR]

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections. [ABSTRACT FROM AUTHOR]

The topic of dispersive optical solitons is one of the essential areas of telecommunications engineering. This paper presents the nonlinear Schrödinger equation (NLSE) with the cubic-quintic-septic (CQS) law which includes higher-order dispersion terms. This equation examines the dynamics of dispersive optical solitons propagation in nonlinear optical fibers. The presented model is significant in mathematics and theoretical physics sciences because long-distance optical fibers are used in optical communication utilized for transoceanic and intercontinental data transmission. First, the considered equation is transformed into a nonlinear ordinary differential equation (NLODE) using the traveling wave transformation. Then, two powerful techniques, Sinh-Gordon expansion approach and the auxiliary equation method (AEM), based on the homogeneous balance rule, are operated to produce analytical solutions for the NLSE with CQS law. Thus, bright, dark, singular, and periodic-singular soliton solutions are acquired. We demonstrate the three-dimensional (3D) and two-dimensional (2D) representations to interpret the physical behavior of some derived solutions. Besides, we investigate the effects of some parameters in the model with graphical illustrations. Therefore, it can be noted that the obtained soliton solutions have a significant role in soliton dynamics. [ABSTRACT FROM AUTHOR]

This paper tackles the recently introduced (4+1)-dimensional Boiti–Leon–Manna–Pempinelli equation (4D-BLMPE) utilized to model wave phenomena in incompressible fluid and fluid mechanics. Modified extended tanh expansion method (METEM) and the new Kudryashov scheme are implemented to produce analytical soliton solutions for the presented equation. The traveling wave transformation is constructed, and the homogeneous balance principle is utilized to apply the two proposed techniques. Furthermore, the flat-kink, smooth-kink, singular, and periodic singular solutions are successfully extracted. Some produced solutions are illustrated graphically to understand the physical meaning of the presented model. Moreover, for the first time in this study, the effect of model parameters on kink soliton dynamics is examined, and graphical representations are depicted and interpreted. [ABSTRACT FROM AUTHOR]

This paper aims to reveal the effects of the fourth-order dispersion and parabolic law which comes from self-phase modulation on the soliton behavior of the cubic-quartic nonlinear Schrödinger equation (CQ-NLSE) by using the modified new Kudryashov method. First, applying the complex wave transformation, the nonlinear ordinary differential form (NODE) has been obtained. Then, the modified new Kudryashov method (mNKM) has been expressed and applied. In the next step, linear algebraic system has been gained and solved. Then analytical soliton solution of the CQ-NLSE has been derived and checked for accuracy so that it satisfies the main equation. For the obtained solution functions, bright and singular soliton solutions have been gained and their graphical presentations have been made. The effects of both the fourth-order dispersion parameter and the parabolic law nonlinearity on the soliton dynamics have been examined and the necessary comments have been made. To our best knowledge, no such study has been reported for the equation examined. [ABSTRACT FROM AUTHOR]

In this research paper, we take into account the (2 + 1)-dimensional Kadomtsev–Petviashvili equation which is important in the soliton theory of nonlinear physics. To get the desired soliton solutions, the modified F-expansion method using the Riccati equation which has many solution functions, as well as the modified generalized Kudryashov's method, had been effectively implemented. One of the reasons for the preference of the methods is that the proposed methods have been widely used before and they have not been applied to this problem. First, the wave transform is applied to the considered nonlinear partial differential equation (NLPDE), the nonlinear ordinary differential equation (NODE) form and the balancing constant are determined. The next step is to use the auxiliary equation depending on the proposed method to find the solution of the NODE form and to obtain the linear algebraic equation system. The solution of this system gives different solution sets for unknown parameter values. Then, soliton solution functions are constructed by using the suitable solution sets. After testing and confirming that the obtained solution functions satisfy the main equation, the three- and two-dimensional illustrations are depicted. [ABSTRACT FROM AUTHOR]

This study investigates the nonlinear Klein–Gordon equation (KGE). We successfully construct some new topological kink-type, non-topological, singular solitons, periodic waves and singular periodic wave solutions to this nonlinear model by using the extended ShGEEM, rational sine-cosine extended (ERSC), and sinh-cosh (ERSCh) methods. In addition, a numerical method for solving the KGE is described in this paper. We use a combination of two numerical techniques called fictitious time integration method and the group preserving scheme (GPS). Fictitious time integration method converts the main equation into a new problem then the GPS is used to gain the numerical solutions. Few experiments are provided to successfully demonstrate the correctness of the approach. [ABSTRACT FROM AUTHOR]

Purpose: This study includes the examination of the cases where the (1 + 1) -dimensional chiral nonlinear Schrödinger equation also has Bohm potential. This review is not to obtain different soliton solutions for both cases but to obtain a certain type of soliton and to observe the effect of the problem parameters. By using the modified new Kudryashovs scheme. This observation also includes how the soliton behavior is effective by comparing the (1 + 1) -dimensional chiral nonlinear Schrödinger equation (C-NLSE) and (1 + 1) -dimensional chiral nonlinear Schrödinger equation with Bohm potential (C-NLSE-BP), especially by examining the Bohm potential parameter. Methodology: In order to apply the proposed analytical method which is the modified Kudryasovs scheme (m-NKM), as in many studies, the nonlinear partial ordinary differential equation (NLPDE) is first converted into nonlinear ordinary differential equation form (NLODE) by using wave transform. Then, in order to determine which degree the solution function to be proposed will be, the balancing constant is calculated. The next step is to determine the unknown parameters of the problem by applying the m-NKM on NODE, obtaining solution sets, and combine the solution of the Riccati equation, which is the basis of the method, with the proposed solution function and wave transform. Obtaining the optical solution by providing the main NLPDE is the next step that follows this stage. The final stage is the graphical analysis and interpretation of the parameter effect for both problems using the obtained solution function. Findings: The examination of the case with and without Bohm potential was carried out on the behavior of the bright soliton shape, which is one of the basic soliton shapes that many effects can be clearly studied on it. It was successfully shown that both equation parameters and the Bohm potential had a significant effect on the soliton behavior, graphical presentations were made and interpreted in detail. Originality: Such an examination has not been studied before in the literature for the investigated equations. [ABSTRACT FROM AUTHOR]

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies. [ABSTRACT FROM AUTHOR]

In this scientific work, we explore the solutions of an important mathematical model appearing in the nonlinear elastic inhomogeneous Murnaghan's rod (NEIMR) or called doubly dispersive equation (DDE) with a useful and powerful analytical technique; which is the extended Kudryashov method with the Bernoulli–Riccati approach. In our research, we have successfully obtained some important solutions of the above-mentioned model such as topological, nontopological, singular solitons, singular periodic and rational solutions. Using the appropriate values of the parameters, we clearly plotted the solutions of the model, 3D, 2D and contour plots. We think that the method used in the study and the results obtained will be an effective motivation tool for many researchers doing research in this field. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Boussinesq equation which is an important equation and it is widely used in coastal engineering, harbors, shallow seas and water wave to model weakly nonlinear and long wave approximation. Exact traveling wave solutions in such equations are extremely valuable in analytical and numerical theories. To compute the soliton solutions of this model, we employ an enhanced modified extended tanh expansion method. We demonstrate that the characteristics of soliton solutions may reflect the dispersion of propagation on wave fronts and have an acceptable reliance on parameter values. Bright, dark, bright-singular, dark-singular, periodic-bright singular, periodic dark-singular solutions identified and three-dimensional (3D), contour and two-dimensional (2D) layouts are represented graphically. [ABSTRACT FROM AUTHOR]

In this research paper, we scrutinize the novel traveling wave solutions and other solutions with conformable, M-truncated and beta fractional derivatives for the nonlinear fractional Hirota–Maccari system. In order to acquire the analytical solutions, the Riccati–Bernoulli sub-ODE technique is implemented. Presented method is the very powerful technique to get the novel exact soliton and other solutions for nonlinear partial equations in sense of both integer and fractional-order derivatives. Mathematical properties of different kinds of fractional derivatives are given in this paper. A comparative approach is presented between the solutions with the fractional derivatives. For the validity of the solutions, the constraints conditions are determined. To illustrate the physical meaning of the presented equation, the 2D and 3D graphs of the acquired solutions are successfully charted by selecting appropriate values of parameters. [ABSTRACT FROM AUTHOR]

This paper presents the (1+1)-dimensional chiral nonlinear Schrödinger equation (1DCNLSE) and (2+1)-dimensional chiral nonlinear Schrödinger equation (2DCNLSE) that define the edge states of the fractional quantum hall effect. In this paper, we implement the Riccati–Bernoulli sub-ODE method in reporting the solutions of these two nonlinear physical models. As a result of this, some singular periodic waves, dark and singular optical soliton solutions are generated for these models. Some of the acquired solutions are illustrated by three-dimensional (3D) and two-dimensional (2D) graphs utilizing suitable values of the parameters with the help of the MAPLE software to demonstrate the importance in the real-world of the presented equations. [ABSTRACT FROM AUTHOR]

This research paper is dedicated to the investigation of the optical soliton solutions with the power law of self-phase modulation (SPM) and the third-order dispersion (TOD), completely neglecting the chromatic dispersion (CD). The aim is focused on two main points. First, obtaining the straddled soliton solution which permits us to have bright and singular soliton by applying the new Kudryashov (nKM) scheme which was recently introduced as a simple, effective, and reliable method. Second, to observe the influences of the TOD, SPM, and inter-modal dispersion (IMD) on pure-cubic optical soliton dynamics in the absence of the CD. [ABSTRACT FROM AUTHOR]

The extended generalizing Riccati mapping method (EGRM) is used to solve the derivative nonlinear Schrödinger equation (DNLSe) with the dimensionless shape. This method reveals several optical solitons including traveling wave solutions (TWS). The studied solutions are identified in four different families including the hyperbolic, the rational and the trigonometric functions. Evaluations of the method are presented with graphical results obtained from our solutions. [ABSTRACT FROM AUTHOR]

In this study, two integration techniques are employed to reach optical solitons to the (n + 1) -dimensional nonlinear Schrödinger's equation ((n + 1) -NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented. [ABSTRACT FROM AUTHOR]

A new generalized exponential rational function method (GERFM) is used to acquire some new optical solitons of Radhakrishnan–Kundu–Lakshmanan (RKL) equation with Kerr nonlinearity. This equation is used to model propagation of solitons through an optical fiber. The well-known exponential rational function method is also a special case of the GERFM. The results reveal that the mentioned method is efficient and simple for solving different nonlinear partial differential equations. [ABSTRACT FROM AUTHOR]

In this paper, symmetry analysis is performed for the nonlinear Chen–Lee–Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach. [ABSTRACT FROM AUTHOR]

Understanding the mechanical and rupture behavior of orthopedic cement fixing the cup of a total hip prosthesis (THP) to cortical bone is crucial for comprehending the conditions governing prosthesis stability and potential loosening. Consequently, this study employs a three-dimensional finite element method to investigate the mechanical behavior of cement with interfacial cracks at the junction between the cement and cup. Through stress distribution analysis, we identify the initiation points of cracks and examine how stress intensity factors (SIFs) vary across three modes of failure (I, II and III) throughout a walking cycle, particularly concerning the femoral head. Our findings reveal that loading stages cause stable variations in SIFs along the crack front, with the highest values consistently at the second end of the crack. Moreover, the propagation mechanism of interfacial cracks is complex, oscillating between modes of opening and plane shear, linked to the SIFs of modes I and II and the material properties of the cement and cup. Furthermore, mode III behavior mirrors that of mode II, with nearly linear increases in SIFs along the crack front, peaking near the crack’s terminus. Overall, mode III (out-of-plane shear) emerges as the primary fracture mode, indicating a risk of damage to the reconstructed acetabulum from fatigue, despite the SIF values being lower than the fracture toughness of both the cup and the cement. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical exploration of the electronic, structural, and mechanical attributes inherent in three rare-earth-free intermetallic compounds, namely, MnTi, MnZr, and MnHf. Employing density functional theory (DFT) calculations with the Implementation of projector augmented wave (PAW); our investigation adopts the supercell approach to meticulously determine the structural and mechanical properties of these materials. The findings reveal that MnTi and MnZr exhibit intrinsic ductility, positioning them as viable contenders for applications demanding high-strength structures. In contrast, MnHf demonstrates mechanical instability. This study provides promising insights into the mechanical characteristics of MnTi and MnZr, underscoring their potential as sustainable structural materials, given the abundance and non-toxic nature of their constituents. The research findings presented herein contribute to the understanding of rare-earth-free intermetallics, offering valuable information for applications in materials science and engineering. [ABSTRACT FROM AUTHOR]