A Japanese programmer who goes by the name SofiyaCat has created a build of DeSmuME, a Nintendo DS emulator and gotten it running Sony on the PSP.
The photo above shows a screenshot of a PSP running a DS homebrew game called GeoWars. The emulator is still painfully slow, and requires a hacked PSP to install it, but it does prove that it’s possible. The emulator uses the PSP screen in portrait mode to simulate the DS dual screen interface.
http://www.youtube.com/watch?v=G_V3vUht_sIFrankly, I’m not too sure why you’d want to bother with this. The Nintendo DS is already portable and very reasonably priced. Never mind the fact that the PSP doesn’t have a touchscreen.
If you’ve got a spare PSP lying around and are up for the installation challenge, you can pick up a copy here. I found this information over on eXophase, who offers a brief installation guide on their site.