This study derives solitons solutions of the reverse-time nonlocal Davey–Stewartson III equation by the Kadomtsev–Petviashvili hierarchy reduction method and Hirota’s bilinear method. The solutions are expressed as $N\times N$ Gram-type determinants with different parametric reduction conditions. $N$-soliton and line breather solutions on both constant and periodic backgrounds are derived. The dynamics of these solutions are discussed. All possible configurations of these solutions are illustrated for $1\le N\le 4$. Both intersecting and parallel solitons are presented. In particular, the elastic and inelastic collisions of the two parallel-soliton solutions are determined. In the inelastic case, the amplitudes of the solitons change after collision. Moreover, the parametric conditions for determining the inelastic collisions are derived, and all possible types of inelastic behaviors are obtained and displayed.

本研究通过Kadomtsev-Petviashvili层次化约简法和Hirota双线性方法推导了逆时非局部Davey-Stewartson III方程的孤子解。解决方案表示为 $ñ\times ñ$ 具有不同参数归约条件的革兰氏类型行列式。 $ñ$推导了恒定和周期性背景下的孤子和线性呼吸解。讨论了这些解决方案的动态。说明了这些解决方案的所有可能配置，以用于 $\mathrm{1个}\le ñ\le 4$。提出了相交和平行的孤子。特别地，确定了两个平行孤子解的弹性和非弹性碰撞。在非弹性情况下，孤子的振幅在碰撞后发生变化。此外，推导用于确定非弹性碰撞的参数条件，并获得并显示所有可能类型的非弹性行为。