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

Abstract

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.

Keywords

• The rational (1/ϕ′(ξ))-expansion method
• Wave variable transformation
• Nonlinear fractional Schrodinger equation
• Analytic solution
• Soliton