Abstract
We consider the family of 2nd order rogue wave rational solutions of the nonlinear Schrödinger equation (NLSE) with two free parameters. Surprisingly, these solutions describe a formation consisting of 3 separate first order rogue waves, rather than just two. We show that the 3 components of the triplet are located on an equilateral triangle, thus maintaining a certain symmetry in the solution, even in its decomposed form. The two free parameters of the family define the size and orientation of the triangle on the (x,t) plane.
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