  General high-order rogue waves in the nonlinear Schroedinger equation are
derived by the bilinear method. These rogue waves are given in terms of
determinants whose matrix elements have simple algebraic expressions. It is
shown that the general N-th order rogue waves contain N-1 free irreducible
complex parameters. In addition, the specific rogue waves obtained by Akhmediev
et al. (Phys. Rev. E 80, 026601 (2009)) correspond to special choices of these
free parameters, and they have the highest peak amplitudes among all rogue
waves of the same order. If other values of these free parameters are taken,
however, these general rogue waves can exhibit other solution dynamics such as
arrays of fundamental rogue waves arising at different times and spatial
positions and forming interesting patterns.
