This paper is devoted to obtaining some new types of exact solutions of the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation utilizing the Lie symmetry method. All the Lie symmetries, infinitesimal generators, and possible geometric vector fields have been obtained by using the invariance condition of the group-theoretic method. Meanwhile, the Lie symmetry reductions and explicit exact solutions are obtained by a one-dimensional (1D) optimal system. All the obtained exact solutions are absolutely new and completely different from the earlier established results in the literature. Moreover, the dynamical behavior of obtained solitons like doubly solitons, dark solitons, kink wave, curved shaped multi-solitons, parabolic waves, solitary waves, and annihilation of elastic multi-soliton profiles is depicted graphically via interesting 3D-shapes. That will be widely used to provide many more attractive complex physical phenomena in the fields of plasma physics, statistical physics, fiber optics, fluid dynamics, condensed matter physics, and so on. Finally, we have verified all the achieved soliton solutions through symbolic computations with Mathematica.

中文翻译：

---

孤子的动力学结构和利用李对称分析的(2+1)维DJKM方程的一些新型精确解

本文致力于利用李对称方法获得 (2+1) 维 Date-Jimbo-Kashiwara-Miwa (DJKM) 方程的一些新型精确解。利用群论方法的不变性条件得到了所有的李对称、无穷小生成元和可能的几何向量场。同时，通过一维（1D）最优系统获得李对称约简和显式精确解。所有获得的精确解都是全新的，与文献中早先确立的结果完全不同。此外，获得的孤子的动力学行为，如双孤子、暗孤子、扭结波、弯曲形状的多孤子、抛物线波、孤波、通过有趣的 3D 形状以图形方式描绘了弹性多孤子剖面的湮灭和湮灭。这将被广泛用于在等离子体物理、统计物理、光纤、流体动力学、凝聚态物理等领域提供许多更有吸引力的复杂物理现象。最后，我们通过 Mathematica 的符号计算验证了所有实现的孤子解。