How to phrase omissions correctly in a thesis?
You could explain one case in detail, then cover the other cases by listing what terms to substitute for the other cases. Especially if you're dealing with applying the same equation with different terminology, you could provide a table of which variable is named what in each case.

E.g.


  Because the principles only differ in terminology, only the solid to liquid transition is covered in detail. The equivalent terminology for each transition is in table 3.