In this paper, the $N$-soliton solutions of a generalized (2+1)-dimensional Hirota–Satsuma–Ito equation are obtained by means of the bilinear method. By applying the long wave limit to the $N$-solitons, the $M$-lump waves are constructed. The propagation orbits, velocities and the collisions among the lumps of the $M$-lump waves are analyzed. Three kinds of high-order hybrid solutions are presented, which contain the hybrid solution between lumps and solitons, a 1-lump and 1-breather, and a $m$-breather and $n$-soliton. The results are helpful to explain some nonlinear phenomena of the generalized shallow water wave model.

中文翻译：

---

$\mathrm{中号}$（2 + 1）维Hirota–Satsuma–Ito方程的整体解和混合解

在本文中， $ñ$利用双线性方法获得了广义（2 + 1）维Hirota–Satsuma–Ito方程的孤子解。通过将长波限制应用于$ñ$-孤子 $\mathrm{中号}$形成了集总波。粒子的团块之间的传播轨道，速度和碰撞。$\mathrm{中号}$块状波被分析。提出了三种高阶混合解，其中包括块体与孤子之间的混合体解决方案，1块体与1呼吸器以及$米$-呼吸和 $ñ$-孤子。研究结果有助于解释广义浅水波模型的一些非线性现象。