How can such a wave exist at the surface of the sun? Recently, I came across the following picture from NASA's SOHO observatory:

It seems evident that this is a transverse wave (mind the 
ring which is bright and dark). But how can this be the case if the
sun consists of gaseous matter? 
 A: I agree it looks like a transverse wave - like the ripples on a pond. But I believe you are fooled by a simple thing: the waves you are looking at look like "illuminated ripples" but are in reality just changes in temperature (changes in brightness of the sun's surface).
If you have a shock wave traveling out across the surface of the sun, what happens? The medium (solar plasma) will alternately be compressed and expanded. That is likely to affect the temperature - and I think that's what you are looking at here.
Now if you could somehow believe that there really were "surface ripples" on the sun's surface, that is really no different than the ripples in water on a pond: while the sun is a plasma (not a gas - not at that temperature), its particles are subject to considerable gravity. And the laws of motion for a wave traveling along the surface of a medium subjected to gravity really don't care about the state of matter of the medium - just the differential forces generated by a slope on the surface (which leads to wave propagation).
Either way there is no contradiction - but I'm pretty sure you are looking at changes in intensity/density, not a "transverse wave".
