Propagation of new dynamics of longitudinal bud equation among a magneto-electro-elastic round rod

In this survey, structure solutions for the longitudinal suspense equation within a magneto-electro-elastic (MEE) circular judgment are extracted via the implementation of two one-of-a-kind techniques that are viewed as the close generalized technique in its field. This paper describes the dynamics of the longitudinal suspense within a MEE round rod. Nilsson and Lindau provided the visual proof of the arrival concerning longitudinal waves within thin metal films. They recommended removal of anomalies between the ports concerning emaciated ([Formula: see text] Å) Ag layers preserved on amorphous silica because of being mildly [Formula: see text]-polarized at frequency tier according to the brawny plasma frequency. Anomalies have been due to confusion over the longitudinal waves mirrored utilizing the two borders. The wavelength is connected according to this wave’s property, which is an awful lot smaller than the wave over light. The wave is outstanding only for altogether superfine films. However, metallic movies defended amorphous substrates that are intermittent within the forward levels of their evolution. This made researchers aware of the possibility on getting ready altogether few layers with a desire to discussing the promulgation about longitudinal waves up to expectation colorful each among reverberation or transport on [Formula: see text]-polarized light. The mated options via the use of generalized Riccati equation mapping method or generalized Kudryashov technique show the rule and effectiveness regarding its methods then its ability because of applying one kind of forms over nonlinear incomplete differential equations.

Construction of optical solitons for conformable generalized model in nonlinear media

In the current analysis, the conformable generalized Kudryashov equation of pulses propagation with power non-linearity is processed. The considered higher order equation represents a generalized mathematical model of many well-known ones in nonlinear media. A variety of multiple kinks, bi-symmetry, periodic, singular, bright and dark optical solitons are extracted via the generalized Riccati equation mapping method. Basing on the Riccati differential equation, the theoretical algorithm extracts a number of empirical solutions that do not exist in the literature. The obtained results showed that the present technique is an effective and strong tool for solving nonlinear fractional partial differential equations and produces a very large number of solutions.

Multiple explicit solutions of the 2D variable coefficients Chafee–Infante model via a generalized expansion method

In this work, we do apply a generalized expansion method to the realistic two-dimensional (2D) Chafee–Infante model with time-variable coefficients which is encountered in physical sciences.The key ideas of this method consist in: (i) to choose a nonlinear wave variable in respect to time-variable into the general finite series solution of the governing model; (ii) to take a full advantage from the general elliptic equation introduced as an auxiliary equation which can degenerate into sub-equations such as Riccati equation, the Jacobian elliptic equations, the generalized Riccati equation. Based upon this powerful technique, we successfully construct for the first time several types of non-autonomous solitary waves as well as some non-autonomous triangular solutions, rational or doubly periodic type ones. We investigate the propagation of non-autonomous solitons and we emphasize as well upon the influence of the variable coefficients. We are providing and analyzing a few graphical representations of some specific solutions. The results of this paper will be valuable in the study of nonlinear physical phenomena. The above- mentioned method could be employed to solve other partial differential equations with variable coefficients which describe various complicated natural phenomena.

Dynamic behaviors for a (2 + 1)-dimensional inhomogenous Heisenberg ferromagnetic spin chain system

We investigate a (2 + 1)-dimensional nonlinear Schrodinger equation (NLSE), which describes the spin dynamics of (2 + 1)-dimensional inhomogeneous Heisenberg ferromagnetic spin chain (IHFSC) with bilinear and anisotropic interactions in the semiclassical limit. Miscellaneous new solitons solutions are obtained through the generalized Riccati equation mapping method (GREMM). Moreover, the effects of homogeneity on the soliton propagation and interaction are discussed. The derived structure of the obtain solutions offers a rich platform to better understand the nonlinear dynamics in the ferromagnetic materials.

On the Generalized Simplest Equations: Toward the Solution of Nonlinear Differential Equations with Variable Coefficients

The simplest equations with variable coefficients are considered in this research. The purpose of this study is to extend the procedure for solving the nonlinear differential equation with variable coefficients. In this case, the generalized Riccati equation is solved and becomes a basis to tackle the nonlinear differential equations with variable coefficients. The method shows that Jacobi and Weierstrass equations can be rearranged to become Riccati equation. It is also important to highlight that the solving procedure also involves the reduction of higher order polynomials with examples of Korteweg de Vries and elliptic-like equations. The generalization of the method is also explained for the case of first order polynomial differential equation.

Construction of soliton solutions for modified Kawahara equation arising in shallow water waves using novel techniques

The modified Kawahara equation also called Korteweg-de Vries (KdV) equation of fifth-order arises in shallow water wave and capillary gravity water waves. This study is based on the generalized Riccati equation mapping and modified the F-expansion methods. Several types of solitons such as Bright soliton, Dark-lump soliton, combined bright dark solitary waves, have been derived for the modified Kawahara equation. The obtained solutions have significant applications in applied physics and engineering. Moreover, stability of the problem is presented after being examined through linear stability analysis that justify that all solutions are stable. We also present some solution graphically in 3D and 2D that gives easy understanding about physical explanation of the modified Kawahara equation. The calculated work and achieved outcomes depict the power of the present methods. Furthermore, we can solve various other nonlinear problems with the help of simple and effective techniques.

Some new solutions of the conformable extended Zakharov-Kuznetsov equation using Atangana-Baleanu conformable derivative

The generalized Riccati equation mapping method, coupled with Atangana?s conformable derivative is implemented to solve non-linear extended Zakharov-Kuznetsov equation which results in producing hyperbolic, trigonometric and the rational solutions. The obtained results are new and are of great importance in engineering and applied sciences.