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

Hong-Juan Tian,Da-Jun Zhang

Figure 5. Double-pole solution (3.11a) of the equation (2.53), with ${l}_{1}=1+0.5{\rm{i}},\,{\beta }_{1}(t)=8\sin t,{\eta }_{1}^{(0)}=1$ and t = 0. (a) Shape of u. (b) Density plot of (a) where the bright stripes stand for singularities.