  An analytical method for constructing various coherent localized solutions
with short-lived characteristics is proposed based on a novel self-mapping
transformation of the (2+1) dimensional KdV equation. The highlight of this
method is that it allows one to generate a class of basic two--dimensional
rogue waves excited on zero-background for this equation, which includes the
line-soliton-induced rogue wave and dromion-induced rogue wave with
exponentially decaying as well as the lump-induced rogue wave with
algebraically decaying in the -plane. Our finding provides a proper candidate
to describe two-dimensional rogue waves and paves a feasible path for studying
rogue waves.
