I will try to keep it a simple and short answer.
- Is it possible to explain in simple terms what makes these waves happen?
The combination of solar activity (solar wind), Mars atmosphere and what is left of Mars magnetosphere.
- Is a similar or at least related phenomenon detectable in Earth's atmosphere?
Yes actually there is one called Aurora Borealis or Northern lights.
In addition ask yourself another question since the Mars effect is in the UV zone thus above the visible (by humans) EM spectrum.
How would Earth look like under the "eyes" of an Ultraviolet Imaging
I have not found any images related to that question, so i would say that i would expect to see something in the UV zone in Earth also.
Furthermore i think you will find interesting that there is also a similar effect in Saturn. One of the many findings of Cassini's mission.
Trying to answer the following question that became for me more clear after a relative comment.
Why Mars has this behavior and is pulsing 3 exactly times per night?
I have a theory for that phenomenon which i don't know if you will find it accepted as an answer. So here goes...
I think the atmosphere in Mars acts like a giant capacitor that discharges at regular times at the UV spectrum area. How is this possible? Some facts to base the theory:
Mars atmosphere is thin.
The atmosphere of Mars is about 100 times thinner than Earth's (source: space.com), and it
is 95 percent carbon dioxide. Here's a breakdown of its composition,
according to a NASA fact sheet:
- Carbon dioxide: 95.32 percent
- Nitrogen: 2.7 percent
- Argon: 1.6 percent
- Oxygen: 0.13 percent
- Carbon monoxide: 0.08 percent
- Also, minor amounts of: water, nitrogen oxide, neon, hydrogen-deuterium-oxygen, krypton and xenon
At this point we have to insert into our logic the term
Dynamic Equilibrium. The most common example of a
Dynamic Equilibrium is something that happens in a closed can of soda. What is that? The balance between the following reactions per second:
- H2CO3 → CO2 + H2O
- CO2 + H2O → H2CO3
The above facts indicate that there is not much material to recycle in the chain presented in the image below:
And in order to keep the
Dynamic Equilibrium between the gases in the Martian atmosphere there must be a reaction of NO becoming back to NO2, that occurs at the same time in some other part of the planet, such as this one:
2 NO + O2 → 2 NO2
(just remember 0.13% O2, 2.7% N2 exist in Martian atmosphere, Oxygen found in Martian Fe2O3 AKA
rust is not counted - but it is a good clue that Mars had once Oxygen and Iron at surface levels)
Last but not least Mars magnetosphere could be one of the reasons. Why? First of all a Geographical map of the Martian crustal magnetic fields based on the spherical harmonics model by Morschhauser et al.  at 200 km altitude, created from MGS MAG/ER data. The map is centered on the antimeridian with labels showing east longitude for a uniformly spaced 30 • grid. Contours show zero altitude relative the areoid
Despite the fact that Mars no longer has an internal dynamo capable of
generating a large global magnetic field as on Earth, there is
evidence to suggest that Mars may once have had such a dynamo. This is
mainly supported by observations from the American satellite mission
MGS (Mars Global Surveyor), which from 1997 to 2006 measured the
magnetic field of Mars using a small magnetometer from an altitude of
100-400 km above the planet’s surface. These measurements showed the
existence of powerful magnetic crustal fields on the planet’s surface,
far more powerful than those found on Earth.
The presence of these crustal fields gives rise to local
mini-magnetospheres, i.e. small areas where the lines of the magnetic
field locally protect the planet surface from electrically charged
particles. Mini-magnetospheres occur when a magnetic field line is
connected to two different points on the Martian surface, thus
creating a kind of bubble. Between these ‘bubbles’, one end of the
magnetic field lines can be connected to the planet and the other to
the interplanetary magnetic field (IMF). (source: Mars’ magnetic field)
If all off the above are correct (i hope i did not forget to mention anything more) then this phenomenon could occur periodically (3 times per night) and at certain geographical regions, simply because it is following a cycle of events