Khan, K. and Akbar, M.A. (2013) Exact and Solitary Wave Solutions for the Tzitzeica-Dodd Bullough and the Modified KdV-Zakharov-Kuznetsov Equations using the Modified Simple Equation Method. Ain Shams Engineering Journal, 4, 903-909.
https://doi.org/10.1016/j.asej.2013.01.010

has been cited by the following article:

• 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.