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Abstract
In this work, we derive a family of high order rational solitons of the 3-wave resonant interaction (3WRI) equation by utilizing generalized Darboux-dressing transformation. We observe that breathers in the three components display self-similar behaviors in the process of propagation. For the first order rational soliton, it is interesting that the dark soliton component bifurcates so as to generate a peak whose amplitude is three times higher than the surrounding background itself with an infinite life time. It would provide us a way to generate ‘eternal’ large amplitude wave in weakly nonlinear dispersive media. Furthermore, the interactions of two rational solitons are studied.
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