Existing car-following prediction methods mainly optimize trajectory accuracy, while rarely considering whether predicted disturbances propagate realistically along a vehicle platoon. This limitation may lead to accurate but string-unstable predictions. We propose SSP-DMGTimeNet, a physics-constrained learning framework for spatiotemporal trajectory prediction of vehicle platoons. The model combines multi-scale temporal representations with cross-vehicle interaction features to capture complex and time-varying platoon dynamics. A propagation-delay-aware causal attention mechanism explicitly models upstream-to-downstream disturbance propagation by learning response delays between adjacent vehicles and accumulating them along the platoon. In addition, time- and frequency-domain string-stability losses relieve disturbance amplification across both adjacent vehicles and arbitrary sub-platoons during training. Experiments on HighD show that SSP-DMGTimeNet achieves an unstable-window rate of 0.65\% for five-vehicle platoons and a maximum head-to-tail amplification of 0.898 on the ground-truth excitation subset, while maintaining competitive trajectory prediction performance. In zero-shot evaluation on NGSIM US-101 and I-80, the model achieves velocity MAEs of 1.316~m/s and 1.252~m/s, with unstable-window rates of 3.90\% and 4.10\%, respectively. These results demonstrate that incorporating platoon-level physical constraints can effectively balance trajectory prediction accuracy and disturbance propagation stability.

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