  We propose an efficient and accurate solver for the nonlocal potential in the
Davey-Stewartson equation using nonuniform FFT (NUFFT). A discontinuity in the
Fourier transform of the nonlocal potential causes accuracy locking if the
potential is solved by standard FFT with periodic boundary conditions on a
truncated domain. Using the fact that the discontinuity disappears in polar
coordinates, we reformulate the potential integral and split it into high and
low frequency parts. The high frequency part can be approximated by the
standard FFT method, while the low frequency part is evaluated with a high
order Gauss quadrature accelerated by nonuniform FFT. The NUFFT solver has
$O(N\log N)$ complexity, where $N$ is the total number of discretization
points, and achieves higher accuracy than standard FFT solver, which makes it a
good alternative in simulation. Extensive numerical results show the efficiency
and accuracy of the proposed method.
