A Waveshine Infinite is commonly known as the standard Fox combo, and is one of the first things that comes to mind when one thinks of Fox. The Waveshine Infinite can not be done with Falco, as his Shine sends them up. The only place one can really do a Waveshine infinite with Falco is in one of those little holes on his Break the Targets stage, but that's just not going to happen unless you're a) using an AR and b) your opponent is wierd.
Types of Waveshine Infinite
There are two types of the Waveshine Infinte, go figure. One is against a wall and is much easier to perform, but harder to set up. The other is the wall-less infinite and is easier to set up but harder to perform for a long period of time. Both combos will be explained in detail below.
The Wall Infinite
The structure of the combo is very simple. It's basically a stationary waveshine, facing either direction, that traps the opponent against the wall indefinitely. Keep in mind it can only work against characters that do not fall down when shined (see: Waveshine). Except Luigi. Since many characters can quickly attack out of your Wall Infinite, you must shine very quickly. Shine, wavedash down, shine, wavedash, as fast as possible. Characters like Peach, who in particular has a very deadly down smash will be mashing the C-stick if caught in a Wall Infinite, so the Fox must be technically perfect or else he will take a potentially fatal down smash. If for any reason you feel your ability to do this slipping, back off. Best method of escape is a wavedash away from your opponent.
Stages Wall Infinite is possible on: Princess Peach's Castle, Corneria, Pokémon Stadium (On Fire and Rock forms), Mute City (yes, there are brief walls), Onett, Icicle Mountain (don't bother), Rainbow Cruise, Brinstar Depths, Hyrule Temple, Green Greens, Venom, Poké Floats, Big Blue, and Fourside.
The Wall-less Infinite
The Wall-less Infinite is prety much just simple waveshining, and can be done against any characters that do not fall down when shined (see: Waveshine). Except Luigi. This combo is not as hard to set up. A simple shine out of the opponent's attempt to sheild grab will do the trick. Once you land a shine, continue waveshining. There you go; you are now performing the Wall-less Waveshine Infinite. But once you reach the ledge, how do you continue this combo making it "infinite"? Well, from here you have two options: knock them off the edge and earn a kill with following edgeguarding, or if you feel more comfortable with racking up damage for a vertical kill, and confident in your ability, then you may do the following: At a suitable point, wavedash a little farther and walk past your opponent if possible, and start waveshining the other way. That's it. It will take a little practice and wil be very difficult to pull off against high level opponents. There is a very evil variation on this where you shine them in the opposite direction each time. There is another variation called the Shine Chase which is performed against characters who fall down when shined.