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This paper considers the generalized Davey-Stewartson equation that is used to investigate the dynamics of wave propagation in water of finite depth under the effects of gravity force and surface tension. The model is considered in the presence of full nonlinearity. The main objective of this paper is to extract soliton solutions of the generalized Davey-Stewartson equation. Three state-of-the-art integration schemes, namely exp (- Φ (ξ)) -expansion method, the first integral method and the Sine-Gordon expansion method have been employed for obtaining the desired soliton solutions. The proposed methods successfully attain different structures of explicit solutions such as bright, dark, singular, rational and periodic solitary wave solutions. All the newly found solutions are discussed with their existence criteria. The 2D and 3D portraits are also shown for some of the reported solutions. [ABSTRACT FROM AUTHOR]

In this work, (1 + 2)-dimensional chiral nonlinear Schrödinger's equation is considered. The optical soliton solutions for the aforementioned model are extracted in a systematic way. Two robust and efficient integration tools such as the first integral method and the sine-Gordon expansion method are used to extract abundant solution such as dark, bright soliton as well as complexitons. The parametric conditions for the validity of these solutions are also listed along with the solutions. The physical meaning of the geometrical structures for some solutions is discussed for different choices of the free parameters. [ABSTRACT FROM AUTHOR]

In this paper, we present the sine-Gordon expansion method to prepare the mixed dark bright wave patterns to the nonlinear partial differential equations arising in mathematical physics. Then, we apply the proposed method for a credible recourse of two nonlinear physical models: the modified Vakhnenko-Parkes and modified α -equation. These exact solutions comprise the hyperbolic, trigonometric, rational and exponential function with few licentious parameter. The analytical solutions have different physical structures and they are graphically analyzed in order to show their dynamical behavior by means of 2D, 3D and contour plots. [ABSTRACT FROM AUTHOR]

This article presents soliton solutions to a generalized nonlinear Fokas-Lenells equation via the Sine-Gordon expansion method. To uncover the clear picture of the gained solutions, the two and three-dimensional figures for the solutions are given. It is shown that the proposed methodology provides powerful mathematical tools for obtaining the exact traveling wave solutions of different nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave (RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters. [ABSTRACT FROM AUTHOR]

In this study, the closed-form wave solutions has been examined to the space–time fractional simplified Camassa-Holm equation through two potential techniques, namely the sine-Gordon expansion approach and the extended tanh function scheme. The equation explains the dispersion effects of several phenomena, including liquid drop patterning in plasma, fluid flow, fission and fusion processes, acoustics, control theory, etc. The fractional-order equation is transformed into a nonlinear equation through a complex transformation. Diverse solutions are determined, and for specified parametric values, the solutions are graphically assessed by depicting 3D and contour plots that provide kinks, singular kinks, plane-shaped, bell-shaped, and other types of solitons. All derived solutions are substituted into the original equation to ensure their accuracy, and the obtained solutions are compared with existing solutions in the literature to demonstrate their novelty. It is noteworthy that the suggested techniques are reliable, competent, and potential mathematical tools to establish closed-form wave solutions. [ABSTRACT FROM AUTHOR]

Abstract In this work, we investigate the optical solitons to the nonlinear Schrödinger equation (NLSE) with spatio-temporal dispersion (STD) arising in ferromagnetic materials and optical fiber. The integration technique adopted is the Sine–Gordon expansion method (SGEM). In addition, the stability analysis of the model is performed. [ABSTRACT FROM AUTHOR]

Nonlinear evolution equations play a crucial role in modelling various physical phenomena, such as fluid flow dynamics and plasma waves. Among them, the generalized Whitham–Broer–Kaup–Boussinesq–Kupershmidt (WBKBK) system, along with its special cases, has garnered significant attention in the study of soliton theory due to its intricate mathematical structure and broad range of applications. This study explores the properties and behaviour of soliton solutions in the WBKBK system. The study presents six new classes of wavelike solutions of the WBKBK system and investigate the unique characteristics exhibited by dark and anti-dark solitons, as well as the phenomenon of forward and backward propagating solitons in the system. These findings contribute to a deeper understanding of the fundamental dynamics of the WBKBK system and offer valuable insights into soliton solutions of the system. • The generalized Whitham–Broer–Kaup–Boussinesq–Kupershmidt system is studied. • The sine-Gordon expansion method is used to obtain solitary waveform solutions to the system. • The system is characterized by forward and backward propagating kink, antikink and bell-shaped solitary waves. [ABSTRACT FROM AUTHOR]

In this paper, we present new exact solution sets of nonlinear conformable time-fractional coupled Drinfeld-Sokolov-Wilson equation which arise in shallow water flow models, when special assumptions are used to simplify the shallow water equations by means of Sine-Gordon expansion method. We also present an analytical-approximate method namely perturbation-iteration algorithm (PIA) for the system. Basic definitions of fractional derivatives are described in the conformable sense. An example is given and the results are compared to exact solutions. The results show that the presented methods are powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations. [ABSTRACT FROM AUTHOR]

In this paper, the sine–Gordon expansion method (SGEM) and the generalized tanh (GTM) methods are employed to find the optical solitary wave solutions to the perturbed nonlinear Schrödinger equation (PNLSE) with Kerr law nonlinearity describing the propagation of optical solitary waves in nonlinear optical fibers. The dark, bright, dark–bright and dark-singular optical solitary waves are retrieved. Additionally, singular solitary waves are also derived as by-products of the integration scheme. Physical interpretations of the obtained results are demonstrated with interesting figures. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNLSE. [ABSTRACT FROM AUTHOR]

In this paper, using the Painleve property, the traveling wave transformation, and the sine-Gordon expansion method (SGEM), the Tzitzéica type evolution equations in nonlinear optics, including the Tzitzéica equation, the Dodd–Bullough–Mikhailov (DBM) equation, the Tzitzéica–Dodd–Bullough (TDB) equation, and the Liouville equation are studied. As a result, a series of traveling wave solutions for the Tzitzéica type equations are obtained. The efficiency of the solution methodology in exactly solving nonlinear evolution equations is confirmed. [ABSTRACT FROM AUTHOR]

In this article, new solitary wave solutions of (2 + 1)−dimensional soliton equation are constructed. This equation is similar to integrable Zakharov equation in plasma physics. The sine-Gordon expansion method and ( G ′/ G )-expansion method are utilized for a reliable treatment of (2 + 1)-dimensional soliton equation. Many novel solutions such as rational, hyperbolic and complex function solutions are characterized with some free parameters to the problem studied. [ABSTRACT FROM AUTHOR]

In this paper, we seek for the new soliton solutions to the coupled nonlinear Maccari's system by using sine-Gordon expansion method. Sine-Gordon expansion method is based on sine-Gordon Eq. (2.1) and a travelling wave transformation. We obtain new complex hyperbolic functions solutions to this system with help of Wolfram Mathematica 9, we also plot 3-dimensional and 2-dimensional graphics to some obtained solution using the same program in Wolfram Mathematica 9. Finally, we submit a comprehensive conclusions. [ABSTRACT FROM AUTHOR]

New optical soliton solutions for the coupled conformable Fokas–Lenells equation with spatio-temporal dispersion are obtained via Atangana's derivative operator using an integration method. The used method in this article is sine–Gordon expansion method. The obtained solutions include dark, bright, singular as well as periodic waves solitons which are graphically discussed through 2D- and 3D-plots. • The coupled conformable Fokas–Lenells equation with spatio-temporal dispersion is investigated. • The Sine–Gordon expansion method is applied to that equation. • A graphical representation of the obtained soliton solutions is presented. [ABSTRACT FROM AUTHOR]

• Abundant solutions of the electrical transmission lines in mZK equation are found. • Performance was done using the strategy of two different techniques. • Physical explanations are discussed for the obtained solutions. Discrete networks, nonlinear networks, high speed computer data buses, computer network connections, and cable signal distribution are analyzed using the modified Zakharov-Kuznetsov (mZK) equation as a model governing the propagation in the electrical transmission lines. In this study, we establish viable extensive traveling wave solutions with the familiar singular kink type, kink type, bell-type solution, singular bell-type solution, t-type solution, and some advanced soliton solutions through the modified simple equation (MSE) and the sine-Gordon expansion methods. The established solutions are highly stable, resilient and capable to travel long distance. The solutions obtained can determine the voltage and current flow that can be used to design the transmission lines. The density plot and three-dimensional diagrams of the solutions obtained illustrate the voltage and current distributions in the transmission line. The traveling wave solutions are found in closed-form which simplify their utilization. The implemented methods are compatible for the extraction of traveling wave solutions. [ABSTRACT FROM AUTHOR]

• The broad-ranging general stable soliton solutions to some nonlinear equations have been established associated with parameters and integral constants in physics and gas dynamics. • The characteristics of gas flow ensuing shock fronts and nonlinear optics have been analysed. • The 3D and contour plots of the obtained solutions are depicted to illustrate profile of the phenomena. Stable soliton solutions for the nonlinear Klein–Gordon equation in condensed matter physics, particle physics, nonlinear optics, solid state physics and the gas dynamics equation ensuing in shock fronts have been established by putting use of the sine-Gordon expansion procedure. We establish the broad-ranging familiar stable wave solutions related with some free parameters, for particular values of which some of the subsisting solutions in the literature are re-established and several fresh solutions are formulated. The contour and 3D shapes are depicted to describe the physical phenomena of the established solutions. Scores of solitary wave solutions are obtained such as, compacton, smooth soliton, anti-bell type solitary wave, bell-type solitary wave, kink and some other new types of solitary wave solutions. The obtained results might play important role in optics, quantum mechanics, mathematical physics and engineering. It is noticeable to inspect that the sine-Gordon expansion procedure is an efficient, competent and straightforward mathematical tool to ascertain exact solitary wave solutions. [ABSTRACT FROM AUTHOR]