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

Hong-Juan Tian,Da-Jun Zhang

Figure 4. Vertical two line soliton solution (3.8a) of equation (2.52), with ${l}_{1}=1,{l}_{2}=0.5,{\beta }_{1}(t)=8\sin t+8{a}_{1}({a}_{1}^{2}-3{b}_{1}^{2})-1$, ${\beta }_{2}(t)=8{a}_{2}({a}_{2}^{2}-3{b}_{2}^{2}),{\eta }_{1}^{(0)}={\eta }_{2}^{(0)}=0$ and fixed t = π/2. (a) Shape of u. (b) 2D plot of (a) at y = 0 and t = 0 (red solid curve), t = π/2 (blue solid curve), t = π (blue dot-dashed curve), t = 5.3 (red dashed curve) and t = 6 (black dashed curve).