B. Buffoni and G.R. Burton. On the stability of travelling waves with vorticity obtained by minimization. NoDEA Nonlinear Differential Equations Appl. 20 (2013) 1597-1629. online at link.springer.com pdf.
G.R. Burton and J.F. Toland. Surface waves on steady perfect fluid flows with vorticity. Comm. Pure Appl. Math. 64 (2011) 975-1007. journal.