PPubMed16 Sep 2021Cited 6×

Optical Solitons with Beta and M-Truncated Derivatives in Nonlinear Negative-Index Materials with Bohm Potential

Muhammad Bilal Riaz, Jan Awrejcewicz, Adil Jhangeer, Hari Mohan Srivastava

Abstract

'Hari Mohan Srivastava'] In this article, we explore solitary wave structures in nonlinear negative-index materials with beta and M-truncated fractional derivatives with the existence of a Bohm potential. The consideration of Bohm potential produced quantum phase behavior in electromagnetic waves. The applied technique is the New extended algebraic method. By use of this approach, acquired solutions convey various types of new families containing dark, dark-singular, dark-bright, and singular solutions of Type 1 and 2. Moreover, the constraint conditions for the presence of the obtained solutions are a side-effect of this technique. Finally, graphical structures are depicted.

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The study derives new families of optical solitons—including dark, bright, and singular types—in nonlinear negative-index materials using beta and M‑truncated fractional derivatives with a Bohm potential via a new extended algebraic method.

What’s new

i.Applied the new extended direct algebraic method to the fractional nonlinear Schrödinger equation with beta and M‑truncated derivatives.
ii.Discovered new families of soliton solutions (dark, dark‑bright, dark‑singular, and singular types) in negative-index metamaterials with a Bohm potential.
iii.Derived constraint conditions for solution existence (a>0 and b‑κθ₃<0).
iv.Provided graphical analysis showing how the fractional parameter μ influences soliton amplitude for both derivative definitions.

How they did it

The authors transformed the governing fractional NLSE into an ordinary differential equation using a wave substitution, then assumed a series solution in terms of a function Z(η) that satisfies a Riccati‑type ODE. They solved the resulting algebraic system with Maple to obtain explicit soliton expressions for both beta and M‑truncated derivatives and illustrated the solutions graphically.

What they found

Parameter values used in figures: B=e, a=2.5, μ=0.9, ω=1, b=1, κ=2.3, α=1.2, β=6, γ=2.9, θ₃=2.7, ν=4, m=1, n=1.
Amplitude of solitons increases with μ for the beta derivative and decreases with μ for the M‑truncated derivative.
Constraint conditions for solution existence: a>0 and b‑κθ₃<0.

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