General Higher-Order Breather and Hybrid Solutions of the Fokas System

Ting-Ting Chen,Peng-Yan Hu,Jing-Song He

Fig.3 Three types of the second-order breather $|U|$ associated with Eqs.(5) and (11) of the Fokas system in the $(x,y)$-plane at $t=0$ with parameters $\eta_{1}^{0}=\pi$, $\eta_{3}^{0}=-{\pi}/{2}$: (a) $P_{1}=ii/{3}$, $P_{3}=-ii/{3}$, $Q_{1}={1}/{3}$, $Q_{3}={1}/{2}$. (b) $P_{1}={1}/{3}$, $P_{3}={1}/{3}$, $Q_{1}=ii/{3}$, $Q_{3}=ii/{2}$. (c) $P_{1}=ii/{3}$, $P_{3}={1}/{3}$, $Q_{1}={1}/{3} $, $Q_{3}=ii/{2}$.