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This study delves into utilizing the Kudryashov auxiliary equation method on the time-fractional (3+1)-dimensional Sasa–Satsuma equation, pivotal for transmitting ultra-fast pulses in optical fibers. The main aim is to generate a variety of optical solitons for the time-fractional nonlinear (3+1)-dimensional Sasa–Satsuma model, including dark, bright, singular, and straddled solitons. These solitons are derived from exponential and hyperbolic function-type solutions, presenting novel findings not previously reported. The study demonstrates the effectiveness of the implemented method in deriving analytical solutions for fractional differential equations. The (3+1)-dimensional Sasa–Satsuma model's potential in optical fiber transmission is highlighted, offering significant insights into generating optical solitons and their applications. [ABSTRACT FROM AUTHOR]

A key objective of the paper is to study the dynamical system for the two types of Sasa–Satsuma equations, namely; Sasa–Satsuma equation and higher-order Sasa–Satsuma equation. A Sasa–Satsuma equation is used to describe the propagation of femtosecond pulses through optical fiber systems. The bifurcation and chaotic characteristic of the Sasa–Satsuma equation and higher-order Sasa–Satsuma equation that arises in fluid dynamics and nonlinear optics are studied. For both models, by using the theory of planar dynamical system the bifurcation and chaotic characteristic of the Sasa–Satsuma equation and higher-order Sasa–Satsuma equation that arises in fluid dynamics and nonlinear optics are studied. For a better understanding of these dynamical behaviors, phase portraits in 2D and 3D figures are dawn. For both equations, the equilibrium points and their effects on the bifurcation behavior are analyzed. Moreover, from the presented results, both models have different dynamical behavior. [ABSTRACT FROM AUTHOR]

In this work, we utilize the improved modified extended tanh method to get optical solitons and other exact solutions for (3+1) dimensional Sasa–Satsuma model with third order dispersion that describe the dynamics of ultrashort pulses in the optical fibers. Many exact solutions are raised with the aid of the proposed method. These solutions include bright solitons, dark solitons, singular solitons, periodic wave solutions, hyperbolic wave solutions, Weierstrass elliptic solutions and Jacobi elliptic solutions. [ABSTRACT FROM AUTHOR]

This research explores a particular form of higher order fractional nonlinear Schrödinger equation termed as the fractional Sasa–Satsuma (FSS) equation. The suggested model has been investigated using the extended ( G ′ G 2 ) -expansion approach and (exp (− ϕ (ξ))) -expansion approach. The fractional behavior of the governing model has been studied using the beta fractional derivative. The fractional Sasa–Satsuma equation plays a significant role in the theory of telecommunications and optical fibers. The proposed analytical techniques successfully extract hyperbolic, rational and trigonometric solutions. The modulation instability has also been carried out in this paper using linear stability analysis. The dynamics of the extracted solutions have been examined by 3D plots and line plots. The extracted results have significance importance in reducing the mitigate internet bottleneck problem found in telecommunications industry. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINNs) can be used to predict various solutions of nonlinear partial differential equations in diverse physical fields. We use the PINNs to predict the (single-) double-hump soliton, multi-hump breather, anti-dark soliton, Mexican-hat soliton, twisted rogue-wave pairs and rational W-shaped soliton of the Sasa–Satsuma equation in optical fibers and deep water wave. The L 2 relative error of the prediction results can achieve high accuracy even with only less training data and training time while the results show that the prediction error will increase with the increase of prediction time. In addition, we employ the PINNs to investigate the parameter discovery of the Sasa–Satsuma equation via the Mexican-hat soliton solution. For the anti-dark soliton, we compare the predicted results and the amount of data for the PINNs method and the traditional split-step Fourier technique, and show that the PINNs method requires less data with the same accuracy of prediction results. • Data-driven solutions of the Sasa–Satsuma equation. • Data-driven parameters discovery of the Sasa–Satsuma equation. • Compared with the split-step Fourier technique, the PINNs method requires less data with the same accuracy of prediction results. [ABSTRACT FROM AUTHOR]

This paper mainly studies the optical soliton solutions of the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity describing the propagation of femtosecond pulses in optical fibers. Firstly, using traveling wave transformation, the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers is simplified into the coupled nonlinear ordinary differential equations. Secondly, according to the trial method of polynomial of rank homogeneous equation, the optical soliton solutions of coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity can be obtained. Finally, in order to explain the propagation of optical solitons, three-dimensional and two-dimensional diagrams of the obtained solutions are drawn. [ABSTRACT FROM AUTHOR]

This paper studies the Sasa-Satsuma equation, which is used to describe the nonlinear phenomenon of pulse propagation in optical fiber communication. By using the direct integration method, all envelope traveling wave patterns are given, including singular solutions, solitary wave solutions and elliptic function double periodic solutions. These patterns show completely the behaviors of dynamics of the model. [ABSTRACT FROM AUTHOR]

This paper obtains soliton solutions of the Sasa–Satsuma model which governs the propagation of solitons through an optical fiber. Bright, dark, singular and combo-singular soliton solutions are recovered by the application of four integration algorithms. [ABSTRACT FROM AUTHOR]