While many people are still patiently waiting for their Google Wave invite, Google Wave is already available for iPhone, ipod and Android phones. I did try out my account on an ipod and it worked good.
A simple way to wave on your phone is to just surf to wave.google.com, ignore the warning (as it would not be able to detect the browser) and get ready to wave on the site that is optimized for web kit browsers.
Warning message for browser, Once you ignore this error and proceed further, you can see the wave dialog,
Adding friends on wave is easy as well
There is no standalone application yet for wave. You can also bookmark this webpage; so that while surfing through the Google Wave, it will look and feel more like an application. The same wave was also seen on the desktop web application.
Google wave Alpha is what gets displayed on the ipod.