I second getting them a muffler if you have it in your heart...
I get similar problems from my neighbors. Woke up about 4am this Sat. to the
smell of something burning. I figured it was a house fire somewhere in the
city so I closed my windows and went back to sleep.
Later, about 8am I'm out mowing the lawn and the smell is worse. Then I
notice smoke rolling out of the backyard of a neighbor two houses up the
street. I walk up there to investigate figuring there might be a smoldering
fire in a storage shed or something. To my suprise I look through the fence
and this guy is burning trash in a barrel in the middle of the city!
Is what really got to me is he tried to do it in the wee hours to avoid
detection, so he must have known it was illegal. Makes me wonder what he
was burning. I announced my displeasure as I walked off and commented as to
the legality of burning in the city.
Only a few minutes later there was no more smoke, so simply voicing my
displeasure was enough. I intended to call the fire dept. but the
non-emergency # was disconnected! At this point I had too much to do,
relatives visiting, so I blew it off.