Dynamics of Different Nonlinearities to the Perturbed Nonlinear Schrödinger Equation via Solitary Wave Solutions with Numerical Simulation

Abstract

This paper investigates the solitary wave solutions for the perturbed nonlinear Schrödinger equation with six different nonlinearities with the essence of the generalized classical derivative, which is known as the beta derivative. The aforementioned nonlinearities are known as the Kerr law, power, dual power law, triple power law, quadratic–cubic law and anti-cubic law. The dark, bright, singular and combinations of these solutions are retrieved using an efficient, simple integration scheme. These solutions suggest that this method is more simple, straightforward and reliable compared to existing methods in the literature. The novelty of this paper is that the perturbed nonlinear Schrödinger equation is investigated in different nonlinear media using a novel derivative operator. Furthermore, the numerical simulation for certain solutions is also presented.

Diverse optical solitons to nonlinear perturbed Schrödinger equation with quadratic-cubic nonlinearity via two efficient approaches

“…Gepreel constructed exact soliton solutions by capitalizing multiple ansatz methods such as rational solitary wave method, q-deformed hyperbolic function, and q-deformed trigonometric function. A. Zafar et al investigated solitary wave solutions for the governing model by means of the Modified Extended tanh Expansion Method [32]. Our research manipulated this study to execute two approaches, new rational extended ShGEEM and the generalized y v -( ( )) exp -expansion method.…”

“…It also has numerous applications in mathematical finance, fluid dynamics, plasma physics, biochemistry, nuclear physics, superconductivity describing solitary wave propagation in piezoelectric semiconductors, condensed matter, solid-state physics characterizing the propagation of a heat pulse in a solid, and so on [36][37][38][39]. Consider the following dynamical model which is known as perturbed nonlinear Schrödinger [32], that can be used to describe some interesting (1+1)-dimensional waves of optics,…”

Regarding on the Results for the Fractional Clannish Random Walker’s Parabolic Equation and the Nonlinear Fractional Cahn-Allen Equation

“…Nonlinear fractional mathematical models (NLFMMs) are broadly implemented to express lots of significant phenomena and nonlinear dynamic applications in applied mathematics, mathematical physics, engineering, signal processing, electromagnetics, communications, acoustics, genetic algorithms, viscoelasticity, robotics, electrochemistry, transport systems, material science, finance, image processing, stochastic dynamical systems, biology, plasma physics, chemistry, nonlinear control theory, and so many. In accordance with determining the exact answers of NLFMMs, countless influential and well-organized schemes have been presented and industrialized, such as the variation of ðG ′ /GÞ-expansion scheme [1], modified ðG ′ /GÞ-expansion technique [2][3][4][5], the first integral technique [6], gener-alized Kudryashov technique [7], fractional subequation scheme [8,9], improved fractional sub-equation scheme [10], generalized exponential rational task scheme [11], novel extended direct algebraic method [12], Sine-Gordon expansion technique [13], subequation scheme [14], Kudryashov technique [15], Jacobi elliptic task scheme [16], exp-task scheme [17], the Jacobi elliptic ansatz method [18], natural transform method [19], fractional iteration algorithm [20,21], the unified method [22], the hyperbolic and exponential ansatz method [23], ð1/G′Þ-expansion scheme [24], modified decomposition method [25], the quintic B-spline approaches [26], an efficient semianalytical algorithm [27], the Jacobi elliptic function expansion (JEFE) method [28], the Lie symmetry technique [29], Hirota's simple method [30,31], the modified extended tanh expansion method [32], exponential finite difference method …”

Superposition solutions to a (3+1)-dimensional variable-coefficient Sharma-Tasso-Olver-Like equation

“…It is necessary to find the solutions of the nonlinear evolution equations. Many mathematicians and researchers have found Lump solutions, soliton solutions, breather solutions and interaction solutions [26][27][28][29][30][31][32][33][34]. The methods of looking for solutions are used widely, including Darboux transformation method [35,36], the ( ¢ G G)-expansion method [37][38][39], inverse scattering transformation method [40,41], Hirota bilinear method [42][43][44][45][46][47], variable separation method [48][49][50][51][52] and so on.…”