  General rogue waves in the Davey-Stewartson-II equation are derived by the
bilinear method, and the solutions are given through determinants. It is shown
that the simplest (fundamental) rogue waves are line rogue waves which arise
from the constant background in a line profile and then retreat back to the
constant background again. It is also shown that multi-rogue waves describe the
interaction between several fundamental rogue waves, and higher-order rogue
waves exhibit different dynamics (such as rising from the constant background
but not retreating back to it). A remarkable feature of these rogue waves is
that under certain parameter conditions, these rogue waves can blow up to
infinity in finite time at isolated spatial points, i.e., exploding rogue waves
exist in the Davey-Stewartson-II equation.
