Open AccessWave Structures for Nonlinear Schrodinger Types Fractional Partial Differential Equations Arise in Physical Sciences
Author(s) -
Mst. Nasrin Nahar,
Md. Tarikul Islam,
Diganta Broto Kar
Publication year - 2021
Publication title -
engineering international
Language(s) - English
Resource type - Journals
ISSN - 2409-3629
DOI - 10.18034/ei.v9i2.560
Subject(s) - mathematics , nonlinear system , partial differential equation , schrödinger equation , rational function , mathematical analysis , nonlinear schrödinger equation , ordinary differential equation , fractional calculus , function (biology) , differential equation , transformation (genetics) , trigonometry , trigonometric functions , physics , quantum mechanics , geometry , evolutionary biology , gene , biology , biochemistry , chemistry
Nonlinear partial differential equations are mostly renowned for depicting the underlying behavior of nonlinear phenomena relating to the nature of the real world. In this paper, we discuss analytic solutions of fractional-order nonlinear Schrodinger types equations such as the space-time fractional nonlinear Schrodinger equation and the (2+1)-dimensional time-fractional Schrodinger equation. The considered equations are converted into ordinary differential equations with the help of wave variable transformation and then the recently established rational ( )-expansion method is employed to construct the exact solutions. The obtained solutions have appeared in the forms of a trigonometric function, hyperbolic function, and rational function which are compared with those of literature and claimed to be different. The graphical representations of the solutions are finally brought out for their physical appearances. The applied method is seemed to be efficient, concise, and productive which might be used for further research.
Mathematics Subject Classifications: 35C08, 35R11