The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation are constructed. The soliton molecule does not exist for the usual -dimensional Boussinesq equation. As a special kind of rational solution, the lump wave is localized in all directions and decays algebraically. The lump solution of the higher-order Boussinesq equation is obtained by using a quadratic function. This lump wave is just the bright form by some detail analysis. The graphics in this study are carried out by selecting appropriate parameters. The results in this work may enrich the variety of the dynamics of the high-dimensional nonlinear wave field.

中文翻译：

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高维Boussinesq方程中孤子分子和团簇解的特征。

作为孤子的结合状态的孤子分子在几个领域引起了相当大的关注。在本文中，-维高阶Boussinesq方程是通过在通常情况下引入两个高阶Hirota运算符而构造的-维Boussinesq方程。通过速度共振机理，构造了高阶Boussinesq方程的孤子分子和非对称孤子。孤子分子通常不存在-维Boussinesq方程。作为一种特殊的有理解，集总波在所有方向上都局部化并以代数形式衰减。通过使用二次函数来获得高阶Boussinesq方程的总解。通过一些细节分析，这块浪潮只是明亮的形式。本研究中的图形是通过选择适当的参数来进行的。这项工作的结果可能会丰富高维非线性波场的动力学变化。