The D’Alembert solution of the wave motion equation is an important basic formula in linear partial differential theory. The study of the D’Alembert wave is worthy of deep consideration in nonlinear partial differential systems. In this paper, we construct a (2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli (eBLMP) equation which fails to pass the Painlev property. The D’Alembert-type wave of the eBLMP equation is still obtained by introducing one arbitrary function of the traveling-wave variable. The multi-solitary wave which should satisfy the velocity resonance condition is obtained by solving the Hirota bilinear form of the eBLMP equation. The dynamics of the three-soliton molecule, the three-kink soliton molecule, the soliton molecule bound by an asymmetry soliton and a one-soliton, and the interaction between the half periodic wave and a kink soliton molecule from the eBLMP equation are investigated by selecting appropriate parameters.

波动方程的D'Alembert解是线性偏微分理论中一个重要的基本公式。在非线性偏微分系统中，对D'Alembert波的研究值得深入考虑。在本文中，我们构造了（2 + 1）维扩展的Boiti–Leon–Manna–Pempinelli（eBLMP）方程，该方程无法通过Painlev属性。通过引入行波变量的一个任意函数，仍然可以得到eBLMP方程的D'Alembert型波。通过求解eBLMP方程的Hirota双线性形式，可以获得应满足速度共振条件的多孤波。三孤子分子，三扭孤子分子，不对称孤子和单孤子结合的孤子的动力学，