  In this paper, we study the existence of rotating and traveling-wave
solutions for the generalized surface quasi-geostrophic (gSQG) equation. The
solutions are obtained by maximization of the energy over the set of
rearrangements of a fixed function. The rotating solutions take the form of
co-rotating vortices with $N$-fold symmetry. The traveling-wave solutions take
the form of translating vortex pairs. Moreover, these solutions constitute the
desingularization of co-rotating $N$ point vortices and counter-rotating pairs.
Some other quantitative properties are also established.
