Assorted soliton structures of solutions for fractional nonlinear Schrodinger types evolution equations

• Published in: Journal of ocean engineering and science 2022-12, Vol.7 (6), p.528-535
• Main Authors: Islam, Md. Tarikul, Akbar, Md. Ali, Gómez-Aguilar, J.F., Bonyah, E., Fernandez-Anaya, G.
• Format: Article
• Language: English
• Subjects: Analytic solution; Nonlinear fractional Schrodinger equation; Soliton; The rational (1/ϕ′(ξ))-expansion method; The rational [formula omitted]-expansion method; Wave variable transformation
• ISSN: 2468-0133; 2468-0133
• DOI: 10.1016/j.joes.2021.10.006

•The (2 + 1)-dimensional time-fractional nonlinear Schrodinger equation and the (1 + 1)-dimensional space-time fractional nonlinear Schrodinger equation are studied.•The rational (1/ϕ′(ξ))-expansion method was considered to obtain closed analytic solutions.•On the basis of the conformable fractional derivative, a composite wave variable conversion has been used to adapt the equations.•Graphical representations illustrating various physical appearances of wave structures. Fractional order nonlinear evolution equations have emerged in recent times as being very important model for depicting the interior behavior of nonlinear phenomena that exist in the real world. In particular, Schrodinger-type fractional nonlinear evolution equations constitute an aspect of the field of quantum mechanics. In this study, the (2 + 1)-dimensional time-fractional nonlinear Schrodinger equation and (1 + 1)-dimensional time-space fractional nonlinear Schrodinger equation are revealed as having different and novel wave structures. This is shown by constructing appropriate analytic wave solutions. A successful implementation of the advised rational (1/ϕ′(ξ))-expansion method generates new outcomes of the considered equations, by comparing them with those already noted in the literature. On the basis of the conformable fractional derivative, a composite wave variable conversion has been used to adapt the suggested equations into the differential equations with a single independent variable before applying the scheme. Finally, the well-furnished outcomes are plotted in different 3D and 2D profiles for the purpose of illustrating various physical characteristics of wave structures. The employed technique is competent, productive and concise enough, making it feasible for future studies.