Abstract
We present first, second, and third order rogue wave (RW) solutions of general two coupled nonlinear Schrödinger equations. We construct higher order RW solutions through a modified Darboux transformation method. In the first iteration we construct a first order RW solution. The solution obtained in the first iteration (first order RW) has been considered as the seed solution to generate the second iterated solution (second order RW). The latter has been given as the seed solution to generate the third iterated solution (third order RW). We also briefly discuss the characteristics of these RWs.
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