Obtaining the soliton solutions of local M-fractional magneto-electro-elastic media

Abstract

In this research paper, the generalized projective Riccati equations method (GPREM) is applied successfully to procure the soliton solutions of the local M-fractional longitudinal wave equation (LWE) arising in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic circular rod (MEECR). Applying a wave transformation to the local M-fractional LWE, the equation can be turned into a set of algebraic equations. Solving the algebraic equation system, we procure the soliton solutions of the local M-fractional LWE. Both the obtained solution functions in the study and the graphical simulations depicted for these functions. It will assist researchers working in this field in the physical interpretation of this equation. Moreover, the reported solutions propose a rich platform to examine the local M-fractional LWE.

Keywords: GPREM; Soliton; The longitudinal wave equation; Truncated M-fractional derivative (t-MFD).

Figure 1

The views in 3D, 2D, contour of ψ₁(x,t) for λ = 1,ω = −0.5,c₀ = 2,p = 4,μ = 3, β = 0.95.

Figure 2

The plots in 3D, 2D, contour of ψ₁(x,t) for λ = 1,ω = −1.1,c₀ = −1,p = −1,μ = 1, β = 0.95.

Figure 3

3D, contour, 2D depictions of ψ₂(x,t) for λ = 1,ω = −1.1,c₀ = 2,p = 4,μ = 0.5 and β = 0.99.

Figure 4

The graphics in 3D, contour, 2D of ψ_3,1(x,t) for λ = −0.5,ω = 1,χ = 0.8,p = 1,μ = 5, β = 0.90.