High-order rogue waves in vector nonlinear Schrödinger equations

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Figure 1

(a), (b) The rhombus structure for the second-order vector RW which contains four fundamental ones. The parameters are $f_1=0$, $f_2=0$, $g_1=1$, $g_2=0$, $h_1=0$, $h_2=10000$. (c), (d) The rectangle structure for the second-order vector RW which contains four fundamental ones. The parameters are $f_1=0$, $f_2=0$, $g_1=1$, $g_2=1000$, $h_1=10$, $h_2=0$.

Figure 2

(a), (b) The triangle structure for the second-order vector RW which contains four fundamental ones. The parameters are $f_1=0$, $f_2=100$, $g_1=1$, $g_2=0$, $h_1=0$, $h_2=0$. (c), (d) The line structure for the second-order vector RW which contains four fundamental ones. The parameters are $f_1=0$, $f_2=0$, $g_1=1$, $g_2=0$, $h_1=10$, $h_2=0$.

Figure 3

(a), (b) The pentagon structure for the second-order vector RW which contains six fundamental ones. The parameters are $f_1=1$, $f_2=0$, $g_1=0$, $g_2=0$, $h_1=0$, $h_2=10000$. (c), (d) The rectangle structure for the second-order vector RW which contains six fundamental ones. The parameters are $f_1=1$, $f_2=0$, $g_1=0$, $g_2=0$, $h_1=100$, $h_2=0$.

Figure 4

(a), (b) The triangle structure for the second-order vector RW which contains six fundamental ones. The parameters are $f_1=1$, $f_2=0$, $g_1=10$, $g_2=0$, $h_1=0$, $h_2=0$ . (c), (d) The line structure for the second-order vector RW which contains six fundamental ones. The parameters are $f_1=1$, $f_2=0$, $g_1=0$, $g_2=0$, $h_1=0$, $h_2=0$.