  In natural and social science, many events happened at different space-times
may be closely correlated. Two events, $A$ (Alice) and $B$ (Bob) are defined
correlated if one event is determined by another, say, $B=\hat{f}A$ for
suitable $\hat{f}$ operators. Taking KdV and coupled KdV systems as examples,
we can find some types of models (AB-KdV systems) to exhibit the existence on
the correlated solutions linked with two events. The idea of this report is
valid not only for physical problems related to KdV systems but also for
problems described by arbitrary continuous or discrete models. The parity and
time reversal symmetries are extended to shifted parity and delayed time
reversal. The new symmetries are found to be useful not only to establish
AB-systems but also to find group invariant solutions of numerous AB-systems. A
new elegant form of the $N$-soliton solutions of the KdV equation and then the
AB-KdV systems is obtained. A concrete AB-KdV system derived from the nonlinear
inviscid dissipative and barotropic vorticity equation in a $\beta$-plane
channel is applied to the two correlated monople blocking events which is
responsible for the snow disaster in the winter of 2007/2008 happened in
Southern China.
