High-Order Line-Soliton Interactions and Anomalous Scattering of Lumps in a (2+1)-Dimensional Reverse Space–Time Nonlinear Schrödinger Equation

This study presents a systematic investigation of nonlinear wave interactions in a (2+1)-dimensional nonlinear Schrödinger equation with a space–time-symmetric potential. We focus on the interaction dynamics of high-order line-soliton solutions and on the anomalous scattering phenomena exhibited by high-order lump solutions, which correspond to fully localized spatiotemporal optical wave packets. Using the generalized Darboux transformation, we obtain, for the first time, explicit high-order line-soliton solutions for this model. A rigorous asymptotic analysis framework is developed to characterize the behavior of these solutions on both long and short time scales. Furthermore, high-order lump solutions are constructed, and their decomposition and anomalous scattering properties are elucidated. This work provides new insights into complex wave dynamics in higher-dimensional integrable systems and their implications for multidimensional beam propagation in nonlinear optical media.