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

Hong-Juan Tian,Da-Jun Zhang

Figure 1. 1-soliton solution of the equation (2.52). (a) Shape of u given in (3.3a) with ${l}_{1}=0.5+0.2{\rm{i}},{\beta }_{1}(z)=\tfrac{1}{1+{z}^{2}},{\eta }_{1}^{(0)}=0,\,t=0$. (b) Shape of $| {\phi }_{1}{| }^{2}$ given in (3.3b) with ${l}_{1}=0.5+0.2{\rm{i}},{\beta }_{1}(z)=\tfrac{1}{1+{z}^{2}},{\eta }_{1}^{(0)}=0,\,t=0$.