The wave motion equation is one of the fundamental equations to describe vibrations of continuous systems. The D’Alembert solution of the wave motion equation is an important basic formula in linear partial differential equations. The study of the D’Alembert wave deserves deep consideration in nonlinear equations. In this paper, the D’Alembert-type wave of the (2 + 1)-dimensional modified Nizhnik–Novikov–Veselov (mNNV) equation is derived by the Ansätze method. The Hirota bilinear form of the mNNV equation is constructed by introducing the dependent variable transformation. The multi-soliton solution is obtained by solving the corresponding bilinear form. By combining the velocity resonance mechanism, a three-soliton molecule, the interaction between a soliton molecule and one soliton, and the interaction between a soliton–solitoff molecule and one soliton of the mNNV equation are obtained. The dynamics of these solutions are shown by selecting the appropriate parameters. These phenomena for the mNNV equation have not yet been given via other methods.

波动方程是描述连续系统振动的基本方程之一。波动方程的D'Alembert解是线性偏微分方程的重要基本公式。在非线性方程中，对D'Alembert波的研究值得深思。本文通过Ansätze方法推导了（2 +1）维修正的Nizhnik–Novikov–Veselov（mNNV）方程的D'Alembert型波。通过引入因变量变换来构造mNNV方程的Hirota双线性形式。通过求解相应的双线性形式获得多孤子解。通过结合速度共振机理，一个三孤子分子，一个孤子分子和一个孤子之间的相互作用，并获得了孤子-孤立分子与mNNV方程的一个孤子之间的相互作用。通过选择适当的参数来显示这些解决方案的动态。mNNV方程的这些现象尚未通过其他方法给出。