  Imposing the condition that there should be a null Killing spinor with all
the metrics and background field strengths being functions of the light-cone
coordinates, we find general 1/2 BPS solutions in D=11 supergravity, and
discuss several examples. In particular we show that the linear dilaton
background is the most general supersymmetric solution without background under
the additional requirement of flatness in the string frame. We also give the
most general solutions for flat spacetime in the string frame with RR or NS-NS
backgrounds, and they are characterized by a single function.
