What we know about dark matter is that it exerts a gravitational pull, or in general relativity (GR) it acts as otherwise non-interacting matter. We've mapped it's density (in terms of say equivalent grams/$cm^3$), and we observe that it tends to be much higher where there is also other matter nearby, such as in the halo of galaxies, and much less where we also see few galaxies. The mapping of where we find it is consistent with it being matter that however has no electromagnetic nor strong nuclear force interactions. It shows gravitational interactions, just like any mass would. It may interact through the weak nuclear force, but it'd be too weak to observe.
We've mapped it for instance in the Bullet Cluster, see the Wikipedia article and picture at https://en.m.wikipedia.org/wiki/Bullet_Cluster. It shows two groups of galaxies passing through each other, and being slowed down by interactions, but the dark matter is not affected so we know it interacts little with itself or other matter, except gravitationally. We know a lot of things about it. The Bullet Cluster is a great example of why it's got to be different than normal matter, but yet always close to high densities of normal matter.
We know it can't be pure energy, i.e., zero mass particles going at the speed of light, because we see it going along and being around galaxies, and if it was zero mass non interacting particles it would just dissipate and separate from the galactic visible matter.
It cannot be electromagnetic waves as it would interacts with charged particles in many galaxies. It cannot be gravitational waves because again it would separate from the galactic matter.
Also note, gravitational waves peaks and troughs cannot represent either dark matter nor dark energy. The dark matter attracts itself so we see much more in certain areas. It is not interspersed with concentrations of dark energy, alternating or otherwise. Dark energy seems to be a constant density everywhere in the universe. They do not form patterns like waves with dark matter. There is no possible relationship.