We construct families of smooth travelling-wave solutions to the inviscid
surface quasi-geostrophic equation (SQG). These solutions can be viewed as the
equivalents for this equation of the vortex anti-vortex pairs in the context of
the incompressible Euler equation. Our argument relies on the stream function
formulation and eventually amounts to solving a fractional nonlinear elliptic
equation by variational methods

Gravejat, Philippe

Smets, Didier