On complex soliton solutions, complex elliptic solutions and complex rational function solutions for the Sasa-Satsuma model equation with variable coefficients

A mathematical representation that includes probability in describing a system’s development is called a stochastic process. A random variable or noise-containing function is generally employed to represent a stochastic term in a mathematical model. In this paper, we analyze optical soliton (OS) solutions for the well-known Stochastic Biswas–Milovic equation (SBME) with the parabolic law nonlinearity. The Sub-ODE approach is used for this purpose. A variety of new optical soliton solutions are generated, including hyperbolic function, periodic solitons, rational solitons, Jacobi elliptic function (JEF), Weierstrass Elliptic Function (WEF), positive solitons, bright solitons, kink type solitons and dark solitons. Localized solitons, such as bright (positive peaks) and dark (localized dips) solitons, are explained by hyperbolic functions. Localized algebraic waves are represented by rational solitons, even with periodic and doubly-periodic solitons are depicted by JEF and WEF, respectively. Kink solitons represent a variety of nonlinear phenomena by connecting different asymptotic states. Bose–Einstein condensation, fiber optic sensors, plasma physics, optical communication and other fields belong to applications for these solitons. Additionally, we will plot graphs to visually represent the system’s response. To plot some graphs for SBME, we will first import the necessary libraries into Jupyter as a machine learning tool, including matplotlib, scipy.integrate and numpy.

In this work, we survey exact solutions of Sasa–Satsuma equation (SSE). We utilize extended trial equation method (ETEM) and generalized Kudryashov method to acquire exact solutions of SSE. First of all, we gain some exact solutions such as soliton solutions, rational, Jacobi elliptic, and hyperbolic function solutions of SSE by means of ETEM. Furthermore, we procure dark soliton solution of this equation by the help of generalized Kudryashov method. Lastly, for certain parameter values, we draw two- and three-dimensional graphics of imaginary and real values of some exact solutions that we achieved using these methods.

Based on the computerized symbolic computation, a new rational expansion method using the Jacobian elliptic function was presented by means of a new general ansätz and the relations among the Jacobian elliptic functions. The results demonstrated an effective direction in terms of a uniformed construction of the new exact periodic solutions for nonlinear differential–difference equations, where two representative examples were chosen to illustrate the applications. Various periodic wave solutions, including Jacobian elliptic sine function, Jacobian elliptic cosine function and the third elliptic function solutions, were obtained. Furthermore, the solitonic solutions and trigonometric function solutions were also obtained within the limit conditions in this paper.

The current research is about the optical solitons of the Kundu–Mukherjee–Naskar (KMN) equation that are obtained by implementing the two proficient approaches named: the extended Jacobi’s elliptic expansion function method and the expa function method. The aforesaid methods are used for the first time in the KMN equation to obtain novel soliton solutions in terms of Jacobi’s elliptic function solutions, which turn into dark, bright, and periodic solutions later. Also, the rational function solutions of the above-mentioned equation are obtained. The obtained solutions are also graphed and verified with the use of symbolic soft computations. The obtained results may be applied to illustrate the substantial concept of the studious structures as well as other related nonlinear physical structures.

New optical soliton solutions of thin-film ferroelectric material equation via the complete discrimination system method

Multi-breather and high-order rogue waves for the quintic nonlinear Schrödinger equation on the elliptic function background

Optical soliton solutions of unstable nonlinear Schröodinger dynamical equation and stability analysis with applications

Dynamical analysis of optical soliton solutions for CGL equation with Kerr law nonlinearity in classical, truncated [formula omitted]-fractional derivative, beta fractional derivative, and conformable fractional derivative types

Chirped optical soliton and Jacobian elliptic function solutions in a metamaterial waveguide

Dispersive optical solitons in magneto-optic waveguides for perturbed stochastic NLSE with generalized anti-cubic law nonlinearity and spatio-temporal dispersion having multiplicative white noise

Bifurcations and dispersive optical solitons for the nonlinear Schrödinger–Hirota equation in DWDM networks

In this paper, we pay attention to the nonlinear dynamical behavior of ultra-short pulses in optical fiber. The new Hamiltonian amplitude equation is used as a governing model to analyze the pulses. We secure the ultra-short pulses in the forms of bright, dark, singular, combo and complex soliton solutions by the utilization of three of sound computational integration techniques that are protracted (or extended) Fan-sub equation method (PFSEM), the generalized exponential rational function method (GERFM), extended Sinh-Gordon equation expansion method (ShGEEM). Moreover, Jacobi’s elliptic, trigonometric, and hyperbolic functions solutions are also discussed as well as the constraint conditions of the achieved solutions are also presented. In addition, we discuss the different wave structures by the assistance of logarithmic transformation. The findings demonstrate that the examined equation theoretically contains a large number of soliton solution structures. By selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in 3D and 2D profiles. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex phenomena. The resulting solutions are novel, intriguing, and potentially useful in understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including nonlinear optics. Our new results have been compared to these in the literature.

This work retrieves a plethora of optical soliton solutions to the dispersive concatenation model with power-law of self-phase modulation. The implementation of the sub-ODE method and its variations and versions yielded such soliton solutions. The intermediary functions were Weierstrass’ elliptic functions as well as Jacobi’s elliptic functions. Their special cases gave way to soliton solutions. In particular, for Jacobi’s elliptic functions, when the modulus of ellipticity approached unity, the soliton solutions have naturally emerged.

The (2 + 1)-dimensional stochastic coupled nonlinear Schrödinger system with multiplicative white noise has significant effect in several fields as statistical mechanics, ecological systems, nonlinear optics, plasma physics, optical-fiber communications, and so forth. Through this article we will extract variety forms of the analytical solutions that represent the dynamical behaviors of the optical soliton solutions and the other rational solutions as well as the soliton velocity emerged by each method to the suggested model. For this purpose, we will utilize four various techniques namely the generalized Kudryashov schema, the Paul–Painleve approach schema, extended simple equation schema and Ricatti–Bernoulli sub order schema that will be applied individually to explore these various types of these optical soliton solutions. The suggested methods will be implemented independently and parallel. Multiple types of optical soliton solutions are detected in forms like the bright-dark, periodic solitons, W-like soliton, some other traveling wave solutions in forms trigonometric, hyperbolic, Jacobi elliptic rational function and solitary wave solutions are also explored. The 2-D and 3D Figure simulations of the dynamical soliton behaviors of all obtained solutions have been documented. All achieved solutions as well as 2D and 3D plots have been established by Mathematica program.

Stability of kink, anti kink and dark soliton solution of nonlocal Kundu–Eckhaus equation