Search

The fundamental intention of this article is to find several soliton solutions to the generalized Benjamin–Bona–Mahony equation. The fractional derivatives are described in the conformable sense. These solutions are generated using the functional variable approach. Then, we acquire via this technique some distinctive solutions, such as the singular soliton, periodic soliton, bell-shaped soliton, and kink soliton solutions. The fundamental feature of the demonstrated method is that it's convenient and provides precise, effective solutions to nonlinear equations. The solutions given will offer a thorough examination of this model and any associated occurrences. [ABSTRACT FROM AUTHOR]

The current manuscript proposes an innovative approach for obtaining exact solutions to the conformable time-fractional nonlinear differential-difference equations (NDDEs). The fundamental concept of this approach involves the generalized exponential rational function method (GERFM). In this method, the exact solutions include trigonometric and hyperbolic functions. In order to assess this method's efficacy, we consider its application to the conformable time-fractional Hybrid Lattice equation. After solving this model, we provide its dynamic behavior through the 3D, 2D, and Contour graphs. The soliton solutions obtained are used to describe any related physical phenomena. [ABSTRACT FROM AUTHOR]

In this article, we focus on a specific version of the NDDEs which is the relativistic Toda lattice equation. We employ the generalized exponential rational function method on a nonlinear model of surface wave propagation to recognize their diverse singular soliton and multi-soliton wave structures. What is remarkable in this article is the use of graphic diagrams, which have diversified the solutions for solving such equations, leading to a greater understanding of the movements of particles and the strengthening of nonlinear lattice dynamics. The efficiency and strength of the employed method are illustrated, signifying its applicability to a wide spectrum of NDDEs in physical phenomena. [ABSTRACT FROM AUTHOR]

The principal purpose of this research is to utilize the exp-function approach for achieving exact solutions of nonlinear optical fibers, including fractional order in the sense of conformable derivatives. Owing to the algorithm of symbolic computational, Some soliton solutions are obtained, including solitary soliton, singular kink-type soliton, and periodic solitons. These results are generated and developed by using the exp-function. To the greatest of our knowledge, the soliton solutions given in this study could be highly beneficial in comprehending physical phenomena. [ABSTRACT FROM AUTHOR]

In this paper, the generalized rational function procedure was used to produce new solitary solutions to the fractional Jaulent–Miodek hierarchy equation. The equation is shortly called the Jaulent–Miodek equation, which was first derived by Jaulent and Miodek and associated with energy-dependent Schrödinger potentials. The equation is converted into a fourth-order partial differential equation using a transformation. In order, we find some solitary solutions such as soliton, rational and hyperbolic function solutions of Jaulent–Miodek hierarchy equation by the help of generalized exponential rational function procedure. Then, for some parameters, we draw three-dimensional graphics of real values of some exact solutions that we acquired by using this procedure. [ABSTRACT FROM AUTHOR]

This paper studies the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili-Boussinesq (KPB) equation via the Hirota's bilinear form and symbolic computation. Mixed type lump solutions are presented, which include rational function, trigonometric function and hyperbolic function. The propagation and the dynamical behaviors of these mixed type of lump solutions are shown by some three-dimensional and contour plots. [ABSTRACT FROM AUTHOR]

The Kerr law and dual power law Schrödinger equations for obtaining optical soliton solutions are studied. In this paper, we investigate these equations via generalized logistic equation method. These various kinds of solutions are favorable for explaining diverse nonlinear physical phenomena. The outcomes are useful in describing the diffusion of optical solitons. [ABSTRACT FROM AUTHOR]

The present study suggests a large family of optical solutions to the Kundu–Eckhaus model. Modified form of an auxiliary equation approach have been used to set the solution families. Compatible variable transform reduces the governing equation to a non linear ordinary differential equation. The parameters of the predicted solution in finite series form are determined by substitution of the solution into this ODE. The results cover a large family of optical solutions that are determined by implementation of various techniques in the literature. In this perspective, the modifed form of the a auxiliary equation approach is evaluated as a generalization of different methods widely used to construct the solutions. [ABSTRACT FROM AUTHOR]

In this paper, a numerical technique based on matrix collocation method is presented for approximating the solution of the Ambartsumian equation in terms of the shifted Bernoulli polynomials. Shifted Bernoulli operational matrix of differentiation is first derived and then utilized to reduce the problem into a system of linear algebraic equations which can be solved to find the solution. Results are included to demonstrate the validity and applicability of the technique and compared with other methods. These results show the efficiency and accuracy of the presented algorithm and also the physical behaviour of the presented problem over large intervals. [ABSTRACT FROM AUTHOR]

In this present study, new sub-equation method is used to construct exact travelling wave solutions of the Cahn-Hilliard equation (CH). As a consequence, many new general exact travelling wave solutions are obtained including generalized hyperbolic (GH) function, generalized trigonometric (GT) function, exponential function and rational function solutions. Compared with the most existing similar new sub-equation method, the proposed method gives new and more general exact travelling wave solutions. More importantly, the method with the help of symbolic computation prepares a powerful mathematical tool for solving a great many nonlinear evolution equations in mathematical physics. [ABSTRACT FROM AUTHOR]

In this paper, with the aid of the Maple software, the new extended direct algebraic method is used as a powerful method to constructs some new solutions to the well-known nonlinear models, namely, the simplified modified Camassa-Holm equation. The space-time fractional derivatives are defined in the sense of the new conformable fractional derivative. It is shown that the method is straightforward and effective mathematical tool for solving nonlinear evolution equations in mathematical physics and engineering. [ABSTRACT FROM AUTHOR]

This study reveals the dark, bright, combined dark–bright, singular optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. We use two integral schemes in reaching such solutions. The constraints conditions which guarantee the existence of valid solutions are stated. By choosing the suitable values of the parameters involved, we plot the 2-dimensional and 3-dimensional surfaces to some of the obtained solutions. [ABSTRACT FROM AUTHOR]