Bifurcation and symmetry breaking in nonlinear dispersive waves

Abstract

The equation governing four-wave interactions in a nonlinear dispersive system is studied. It is shown that a nonlinear steady-state plane wave can bifurcate into nonplanar steady-state solutions. In the case of an isotropic medium, the bifurcation is degenerate and the bifurcated solutions may preserve or break the symmetry. An example is given of a symmetry-breaking solution for deep-water gravity waves and its stability is discussed.

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