Is there any abbreviation for hydrates?
There is, as far as I know, no shorthand for that, but you might be able to omit it completely in a first order approximation. The closest might be adding $\ce{(aq)}$ when working in aqueous environment.

Adding $\ce{.$x$\,H2O}$ to the formula usually indicates, that it is a solid and that there are $x$ water molecules enclosed in the crystal structure. It depends on what you are looking at, which kind of reaction, what you might be able to omit.

For example, when you are describing a drying process, it is not possible:
$$\ce{\overset{blue}{CuSO4.5H2O} -&gt;[\Delta] \overset{white}{CuSO4} + 5H2O}$$

When you are working in aqueous solution it is usually not important, as there is much more water around it, hence
$$\ce{\overset{blue}{CuSO4.5H2O} + Na2S -&gt; \overset{black}{CuS} v + 2Na+ + SO4^{2-} + 5H2O}$$
is essentially the same as
$$\ce{CuSO4~(aq)  + Na2S~(aq) -&gt;CuS~(s) v + 2Na+ ~(aq) + SO4^{2-}~(s)}$$

If you are describing a redox reaction, it might be the same, hence the following should be fine
$$\ce{CuSO4~(aq) + Zn~(s) -&gt; Cu~(s) v + Zn^{2+}~(aq) + SO4^{2-}~(aq)}$$
Often you can omit the $\ce{(aq)}$ or $\ce{(s)}$ all together.

So depending on what kind of chemistry you are talking about, some information can be implied and therefore be omitted. If you add an example of what kind of reactions/ substances you are working with, I can expand my answer to take that into account.