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Vortex crystals and non-existence of non-axisymmetric solitary waves in the Flierl-Petviashvili equation

We looked for non-axisymmetric, two-dimensional solitary waves for the FlierlPetviashvili equation of geophysical fluid dynamics. We found none and conjecture that none exist. However, we did find that the previously known radially symmetric vortices can organize themselves into regular patterns — vortex crystals — when subject to boundary conditions of spatial periodicity. Beginning from non-solitonic initial conditions, the time-dependent flow rapidly organizes itself into such patterns of monopoles plus a small, dispersing transient.