by $S^2$. Let us see in some detail how this works for the wave. The wave solution is given, in suitable coordinates (light-cone coordinates), by the metric ds\^2 = K dx\^2 + 2dxdt + dy\_i dy\_i, where $K=K(y_i)$ is a harmonic function in the transverse space. One can add such a wave in the direction of a common string in the intersection (in these cases there is an $adS_3$ factor in the near-horizon geometry). For $M2\perp M5$ plus a wave the metric is[@Tse1] ds\^2&=&H\_2\^[-]{}H\_5\^[-]{}(K dx\^2 + 2dxdt) +H\_2\^[-]{}H\_5\^(dx\_2\^2) +H\_2\^H\_5\^[-]{}(dx\_3\^2++dx\_6\^2) &&+H\_2\^H\_5\^(dr\^2 + r\^2 d\_3\^2), where $d\O_3$ is the line element on the unit three-sphere. The harmonic functions are $H_{2,5}=1+{Q_{2,5}\over r^2}$ and $K={Q_W\over r^2}$. Note that adding a constant to $K$ amounts to a coordinate transformation $t\rightarrow t+\a x$. In the near-horizon limit (or after applying the shift transformation) the constants in the harmonic functions drop out and we obtain \[adS3W\] ds\^2 = dx\^2 + d\^2 + 2 e\^[2]{}dxdt + ds\^2\_[E\^5]{}+dØ\_3\^2, where for convenience we have set $Q_2 = Q_5 = Q_W =1$, and we have transformed to a new radial coordinate $\rho=\log{r}$. Thus the metric splits up into a five-dimensional flat space, a three-sphere and the first three terms which constitute 