Some classes of two-dimensional stationary vortex structures in an ideal liquid

New types of plane stationary vortex formations in an ideal liquid are found. These structures are described by exact solutions of the equation for the stream function. This equation is the elliptical analog of the well-known Bullough–Dodd–Gibert–Shabat nonlinear wave equation. The Lyapunov stability of some of the solutions follows from Arnol'd's theorem.