Rogue wave triplets

We consider the family of 2nd order rogue wave rational solutions of the nonlinear Schrodinger 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. (C) 2011 Elsevier B.V. All rights reserved.