Abstract:
The time-fractional nonlinear Schrodinger equation has the following form:....
where dV is the trapping potential and d is a real constant. The physical model
of above equation and its generalized forms arise in various areas of physics,
including quantum mechanics, nonlinear optics, plasma physics and
superconductivity. Exact solutions of most of the fractional nonlinear Schrodinger
equations cannot be found easily. Therefore, analytical and numerical methods have
been used in the literature. Some of the analytical methods for solving nonlinear
problems include the Adomian decomposition method, Variational iteration method
and Homotopy analysis method. In this study, we use the Sumudu decomposition
method to construct the approximate analytical solutions of the time-fractional
nonlinear Schrodinger equations with zero and nonzero trapping potentials. The
Sumudu decomposition method is a combined form of the Sumudu transform and
the Adomian decomposition method. The fractional derivatives are defined in the
Caputo sense. The exact solutions of some nonlinear Schrodinger equations are given
as a special case of our approximate analytical solutions. The computations show that
the described method is easy to apply, and it needs smaller size of computation as
compared to the aforementioned existing methods. Further, the solutions are derived
in a convergent series form which shows the effectiveness of the method for solving
a wide variety of nonlinear fractional differential equations.
