It is an important issue to numerically solve the time fractional
Schr？dinger equation on unbounded domains, which models the dynamics of optical
solitons propagating via optical fibers. The perfectly matched layer approach
is applied to truncate the unbounded physical domain,
and obtain an initial boundary value problem on a bounded computational
domain, which can be efficiently solved by the finite difference
method. The stability of the reduced initial boundary value problem is
rigorously analyzed. Some numerical results are presented to illustrate the
accuracy and feasibility of the perfectly matched layer approach. According to these examples, the absorption parameters
and the width of the absorption layer will affect the absorption effect. The
larger the absorption width, the
better the absorption effect. There is an optimal absorption parameter,
the absorption effect is the best.
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