The splitting mechanism of the second-order rogue wave—Interaction between two component first-order Akhmediev breathers

Abstract

Based on the nonlinear Schrödinger equation, it's illustrated that the peak intensity of Akhmediev breather is negatively correlated with the modulation frequency firstly. Then, two splitting modes of the second-order rogue wave have been studied in detail through the second-order rogue wave train formed by the nonlinear superposition of two first-order Akhmediev breathers whose modulation frequency ratio is 1:2. It is revealed that the process of the mode B splitting can be divided into three stages: the restructuring stage where the intensity of the latter sub-peaks of the main peak decreases first and then increases, the competition stage where the fine structure forms and the relaxation stage. The process of the mode A splitting can be divided into two stages: the restructuring stage and the relaxation stage. And both are due to the interaction between the two first-order component Akhmediev breathers. The results can be used to explain the different characteristics of the two splitting modes of the second-order rogue wave. In addition, the inevitability of the fine structure appearance in the process of the mode B splitting of the second-order rogue wave, which causes the transformation point on the peak intensity curve of the second order rogue wave, is also revealed. We anticipate that it will be a meaningful and novel way to study the characteristics of the high-order rogue wave through interaction between breathers with certain modulation frequency ratio.