General rogue wave solutions under SU(2) transformation in the vector Chen???Lee???Liu nonlinear Schr??dinger equation

We obtain analytically the exact explicit rogue wave solutions up to the second order of the vector Chen-Lee-Liu nonlinear Schrodinger equation, using the generalized non-recursive Darboux transformation method. In terms of these solutions, we demonstrate the fundamental Peregrine solitons as well as their doublet, triplet, quartet, and sextet counterparts on the general periodic backgrounds caused by SU(2) transformation. We numerically confirm that, although the Peregrine solitons sitting on SU(2) periodic backgrounds may suffer from larger disturbances than what they experience on SO(2) periodic backgrounds, such rational solitons developed on either kind of backgrounds can manifest clearly in spite of strong non-integrable perturbations. Other rogue wave topics such as rogue wave coexistence and the related parametric conditions are also discussed. (C) 2022 Elsevier B.V. All rights reserved.