Cauchy matrix structure of the Mel'nikov model of long-short wave interaction

Hong-Juan Tian,Da-Jun Zhang

Figure 3. 2-soliton solutions (3.8) of the equation (2.52), with ${l}_{1}=0.5+0.1{\rm{i}},{l}_{2}=0.8+0.5{\rm{i}}$, ${\beta }_{1}(t)=\sin t,\ {\beta }_{2}(t)=1$, ${\eta }_{1}^{(0)}={\eta }_{2}^{(0)}=0$ and fixed t = 2. (a) Shape of u. (b) Shape of $| {\phi }_{1}{| }^{2}$. (c) Shape of $| {\phi }_{2}{| }^{2}$.