TITLE:
Closed Form Exact Solutions to the Higher Dimensional Fractional Schrodinger Equation via the Modified Simple Equation Method
AUTHORS:
M. Nurul Islam, M. Ali Akbar
KEYWORDS:
Modified Simple Equation (MSE) Method, Fractional Differential Equation, Nonlinear Evolution Equations, Higher Dimensional Schrodinger Equation, Traveling Wave Transformation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.1,
January
11,
2018
ABSTRACT: In this article, we
investigate some exact wave solutions to the higher dimensional time-fractional Schrodinger
equation, an important equation in
quantum mechanics. The fractional Schrodinger equation further precisely describes the quantum state of a physical
system changes in time. In order to determine the solutions a suitable
transformation is considered to transmute the equations into a simpler ordinary
differential equation (ODE) namely fractional complex transformation. We then
use the modified simple equation (MSE) method to obtain new and further general
exact wave solutions. The MSE method is more powerful and can be used in other
works to establish completely new solutions for other kind of nonlinear fractional differential equations arising in mathematical
physics. The affect of obtaining parameters for its definite values which are
examined from the solutions of two dimensional
and three dimensional time-fractional Schrodinger equations are discussed and
therefore might be useful in different physical applications where the
equations arise in this article.