  In this article, we provide a simple method for constructing dispersive
blow-up solutions to the nonlinear Schr\"odinger equation. Our construction
mainly follows the approach in Bona, Ponce, Saut and Sparber [2]. However, we
make use of the dispersive estimate to enjoy the smoothing effect of the
Schr\"odinger propagator in the integral term appearing in Duhamel's formula.
In this way, not only do we simplify the argument, but we also reduce the
regularity requirement to construct dispersive blow-ups. In addition, we
provide more examples of dispersive blow-ups by constructing solutions that
blow up on a straight line and on a sphere.

Analysis of PDEs