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This research paper's primary goal is to find fresh approaches to the Hirota–Maccari system. This system explains the dynamical features of the femto-second soliton pulse in single-mode fibers. The bright soliton, dark soliton, dark-bright soliton, dark singular, bright singular, periodic soliton, and singular solutions are developed utilizing the modified auxiliary equation technique. To make the physical significance of each unique solution clearer, it is mapped in both 2D and 3D. The primary Hirota–Maccari system is being verified by all new solutions, and the constraint condition is also provided. The obtained optical solitons may be important for the analysis of nonlinear processes in optic fiber communication and signal processing. [ABSTRACT FROM AUTHOR]

The modified exponential function method is used to obtain some new analytical solutions of the nonlinear Gerdjikov–Ivanov equation with the M-fractional operator. The novel obtained solutions are expressed in hyperbolic, trigonometric, and exponential function forms. Moreover, the instability modulation and gain spectra of the Gerdjikov–Ivanov equation are also analyzed. Constraints conditions are utilized to verify the existence of the solutions. Presented solutions are novel, satisfy and verify the M-fractional Gerdjikov–Ivanov equation. [ABSTRACT FROM AUTHOR]

This research manuscript focuses on the extraction of dark-bright solitons and periodic wave distributions of two models, namely, the Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation and complex Kundu–Eckhaus equation with conformable derivative. To reach these important properties, the generalized exponential rational function method is considered. To observe wave distributions in periodic and singular sense, dynamical behaviour modulus of solutions are also archived. Strain conditions for validity of results obtained in this paper are also reported. [ABSTRACT FROM AUTHOR]

In this paper, perturbed Chen–Lee–Liu equation is considered to describe pulse propagation in optical fibers. Chen–Lee–Liu equation is a derivative form of the nonlinear Schrödinger equation. Two renowned analytical techniques namely, exp (- φ (η)) -expansion method and the generalized Kudryashov method are applied to analyze this model. The algorithm of these methods is also presented. Different structures of soliton solutions are successfully investigated for perturbed this model. Additionally, constraint conditions on coefficients of perturbation terms are also defined to assure the existence of such solitons. The graphical representation of these solutions is shown to demonstrate the dynamics of pulse propagation governed by Chen–Lee–Liu equation in optical fibers. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the higher-order dispersive extended nonlinear Schrödinger equation, which demonstrates the propagation of ultrashort pulses in optical communication networks. In this study, both the sinh-Gordon expansion method and the generalized exponential rational function method are used to offer some novel optical solutions. These optical soliton solutions are dark soliton, bright soliton, singular, periodic, and dark-bright soliton solutions. The obtained optical soliton solutions are presented graphically in 2D and 3D to clarify the behavior of solutions more effectively. The constraint conditions are also used to verify the exitances of the new analytical solutions. Moreover, all solutions compared to solutions obtained previously are new, and all the new wave solutions have verified Eq. (1) after we substituted them into the studied equation. In the future, these novel soliton solutions will be very helpful in developing fluid dynamics, biomedical issues, dynamics of adiabatic parameters, industrial research, and many other areas of science. To our acknowledgment, the presented optical solutions are novel, and also beforehand these methods have not been applied to this studied equation. [ABSTRACT FROM AUTHOR]

This study applies the powerful sine-Gordon expansion method in acquiring some new solutions to the strain wave equation in micro-structured solids arising in mathematical physics. The strain wave equation in micro-structured solids is used in modelling wave propagation in micro-structured materials. We successfully acquire some new solitary wave solutions with hyperbolic function structure. By taking some suitable values of parameters involved in the solutions, we plot the 2D, 3D and contour graphs of all the obtained solutions in this study. [ABSTRACT FROM AUTHOR]

In this work, two new adaptations for the trigonometric and hyperbolic trigonometric function approaches have been presented. These two modifications, entitled modified extended rational sin – cos function technique and modified extended rational sinh – cosh function method, have been applied for the first time to the Fokas system that represents the nonlinear pulse propagation in monomode fiber optics. We intend to produce innovative, explicit traveling waves, solitons, and periodic wave solutions. These achieved outcomes are presented in the form of exponential functions, trigonometric hyperbolic functions, and combination constructions of the exponential functions along with the trigonometric and hyperbolic trigonometric functions. The obtained solutions reveal significant features of the physical phenomenon and are new. The investigated model incorporates the notions of dispersion, transverse diffusion, degree of dispersion, nonlinear pairing, nonlinear immersion, and the force of the nonlinear interaction among the two components of the system. For the most accurate visual evaluation of the physical importance and dynamic properties, we have presented the findings in a variety of plots, which involve two- and three-dimensional representations. One or more elements in our research that are unique, such as newly modified methodologies, is a new observation that leads researchers to invest in new solutions. [ABSTRACT FROM AUTHOR]

The thermophoretic motion (TM) system with a variable heat transmission factor, based on the Korteweg-de Vries (KdV) equation, is used to model soliton-like thermophoresis of creases in graphene sheets. Painlevé test is employed to discover that the equation is Painlevé integrable. Then an auto-Bäcklund transformation using the truncated Painlevé expansion is obtained. Concerning the additional variables, the auto-Bäcklund transformations convert the nonlinear model to a set of linear partial differential equations. Finally, various explicit precise solutions based on the acquired auto-Bäcklund transformations are investigated and the researched solutions are illustrated in 3D, 2D and contour plots. Furthermore, the Cole-Hopf transformation is used in conjunction with Hirota's bilinear technique to get multiple regular and singular kink solutions. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlinear Schrödinger equation in the sense of conformable derivative. Bifurcations and phase portraits are first proposed by using bifurcation theory, which investigates the dynamical behavior of this equation. This bifurcation theory classifies the plausible solutions to infinite periodic wave solutions, periodic wave solutions, two kink (anti-kink) wave solutions, and two families of breaking wave solutions. A generalized double auxiliary equation approach that generates three families of exact exact traveling wave solutions is then proposed using the conformable operator under various parameter conditions. The 3D behavior of various solutions with absolute real and imaginary parts is displayed. The obtained results show that the proposed methodology is efficient and applicable to a broad class of conformable nonlinear partial differential equations in mathematical physics. [ABSTRACT FROM AUTHOR]

In this paper, we study the generalized higher-order nonlinear Schrödinger equation analytically. We use two integral schemes for conducting this study. Dark, bright, combined dark-bright optical, singular soliton, soliton-like and trigonometric function solutions are successfully constructed. We give the constraint conditions for the existence of valid solutions. The 2D, 3D and the contour graphs for the dark and bright solitons are plotted. [ABSTRACT FROM AUTHOR]

The dynamical systems of soliton propagation through optical fibers for trans-continental and trans-oceanic distances is one of the most interesting areas of study. Optical solitons are restrained electromagnetic waves that stretch in nonlinear dispersive media and allow the intensity to remain unchanged due to the balance between dispersion and nonlinearity effects. In this study, we successfully acquire dark, bright, combined dark-bright, singular and combined singular soliton solutions to the decoupled nonlinear Schrödinger equation arising in dual-core optical fibers by using the extended sinh-Gordon equation expansion method. The constraint conditions for the existence of valid soliton solutions are given. We discuss how change in parameters affect the solitons transmission. We present the 2D, 3D and the contour graphs to some of the reported solutions. [ABSTRACT FROM AUTHOR]

This study acquires the wave solutions of the two well-known nonlinear models, namely; the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The modified Benjamin-Bona-Mahony is a nonlinear model that describes the long surface gravity waves of small amplitude and the coupled Klein-Gordon equation describes the quantized version of the relativistic energy-momentum relation. We successfully acquire some new solutions to these models such as kink-type and soliton solutions in complex hyperbolic functions form. We plot the 3D and 2D surface of the all the obtained solutions in this study. The mathematical approach used in this study is the sine-Gordon expansion method. [ABSTRACT FROM AUTHOR]

This study investigates the Nizhnik-Novikov-Veselov and the Drinfel’d-Sokolov systems by using the extended sinh-Gordon equation expansion method. The Nizhnik-Novikov-Veselov system is an isotropic Lax extension of the one-dimensional Korteweg-de Vries equation and the Drinfel’d-Sokolov system is a nonlinear model that possesses some special forms of Lax pairs. Topological kink-type, topological, non-topological, compound topological-non-topological bell-type and singular soliton solutions are successfully constructed. Under the choice of suitable values of parameters, the 2D, 3D and contour graphs to some of the obtained solutions are plotted. [ABSTRACT FROM AUTHOR]

This study constructs bright and singular optical solitons the (2+1)-dimensional NLSE and the Hirota equation by utilizing the new sine-Gordon expansion method. The parametric conditions for the existence of valid solitons are given. We give the variations of solitary and periodic wave solutions that depend on the parameters. We present the 2D, 3D and contour graphs to represent the kind of solutions secured in this study. [ABSTRACT FROM AUTHOR]

This study investigates the longitudinal wave equation in a magneto-electro-elastic circular rod by using the extended sinh-Gordon equation expansion method. Topological, non-topological and singular soliton solutions are extracted. To illustrate the physical appearance of the obtained solutions, 2D, 3D and the contour graphs to some of the obtained solutions are plotted. The reported results may be useful in explaining the physical meaning of the studied models and other nonlinear physical models arising in nonlinear sciences. [ABSTRACT FROM AUTHOR]