Interaction of two-dimensional localized solutions near a weakly inverted bifurcation

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Abstract
We study the interaction of two-dimensional (2D) solutions as they arise for the envelope equations for a subcritical bifurcation to traveling waves. We show that these 2D localized solutions can collide and reemerge unchanged in size and shape after the collision in contrast to what is found in 2D soliton systems. Various other types of behavior arise as the impact parameter and the cross coupling between the waves are varied. We point out that these phenomena should be observable experimentally for hydrodynamic instabilities in anisotropic liquids such as nematic liquid crystals.