I'm trying to create a curved drop shadow effect with a white/transparent background similair to the photo below.

I was able to generate the following picture with this command:
convert thumb.png \( +clone -background gray -shadow 80x2+0+1 -wave -20x480 \) +swap -background white -layers merge +repage shadow.png
I can't figure out how to swap out the gray background in the picture. I woud like the background to be white/transparent.
Thanks,