Two families of semi-rational solutions to the Mel’nikov equation (ME), which is a known model of the interaction between long and short waves in two dimensions, are reported. These semi-rational solutions describe interaction between lumps and solitons. The first family of semi-rational solutions is derived by employing the KP-hierarchy reduction method. The fundamental (first-order) semi-rational solutions, consisting of a lump and a dark soliton, feature three different interactions, depending on speeds of the corresponding lump, V_lump, and soliton, V_soliton: fusion of the lump into the dark soliton (at V_lump < V_soliton); splitting of the lump from the soliton (at V_lump > V_soliton); and lump-soliton bound states (at $V_{\mathrm{lump}}=V_{\mathrm{soliton}}$). Three subclasses of non-fundamental semi-rational solutions, namely, higher-order, multi-, and mixed semi-rational solutions, are produced. These non-fundamental semi-rational solutions also represent different interaction: fusion of mutli-lumps into mutli-dark solitons, fission of multi-lumps from multi-dark solitons, multi-lump-soliton bound states, partial merger or partial splitting of lumps into/from lump-soliton bound states, etc. In particular, by selecting specific parameter constraints, the first family of semi-rational solutions reduces to solutions of a newly proposed partially spatial-reversed nonlocal ME. The second family of semi-rational solutions is constructed by using the Hirota method combined with a perturbative expansion and a long-wave limit, which describes a lump permanently propagating on the background of a dark soliton. The second family of the solutions indicates not all interactions between lumps and solitons in the ME give rise to fission or fusion. Besides that, a semi-rational solution to the coupled Schrödinger-Boussinesq equation, consisting of a rogue wave and a dark soliton, is obtained as a reduction of a semi-rational solution belonging to the second family.

报告了梅尔尼科夫方程（ME）的两个半理性解，这是二维中长波和短波之间相互作用的已知模型。这些半理性的解决方案描述了团块和孤子之间的相互作用。第一类半理性解决方案是通过采用KP层次简化方法得出的。基波（一阶）半合理的解决方案，由一个块和一个暗孤子，特征的三个不同的相互作用，这取决于相应的块状，的速度V_块，和孤子，V_孤子：块状的融合进入黑暗孤子（V_块 <  V_孤子）; 孤子从孤子分裂（在V_块 >  V_孤子）; 和块孤子束缚态（在$V_{\mathrm{块}}=V_{\mathrm{孤子}}$）。产生了非基本半理性解决方案的三个子类，即高阶，多和混合半理性解决方案。这些非基本半理性解决方案还表示不同的交互作用：将多团融合为多-暗孤子，将多团从多暗孤子中分裂出来，将多团-孤子束缚态，将部分团合并或部分分解。特别是通过选择特定的参数约束，第一类半有理解可简化为新提出的部分空间反转的非局部ME的解。使用Hirota方法结合扰动展开和长波极限来构造第二类半有理解。它描述了一个在黑暗孤子背景下永久传播的肿块。解决方案的第二族表明，ME中块体和孤子之间的相互作用并非全部引起裂变或聚变。除此之外，还获得了由流浪波和暗孤子组成的耦合Schrödinger-Boussinesq方程的半理性解，作为第二类半理性解的简化。