Recently, artificial intelligence (AI)-enabled nonlinear vehicle platoon dynamics modeling plays a crucial role in predicting and optimizing the interactions between vehicles. Existing efforts lack the extraction and capture of vehicle behavior interaction features at the platoon scale. More importantly, maintaining high modeling accuracy without losing physical analyzability remains to be solved. To this end, this paper proposes a novel physics-encoded deep learning network, named PeMTFLN, to model the nonlinear vehicle platoon dynamics. Specifically, an analyzable parameters encoded computational graph (APeCG) is designed to guide the platoon to respond to the driving behavior of the lead vehicle while ensuring local stability. Besides, a multi-scale trajectory feature learning network (MTFLN) is constructed to capture platoon following patterns and infer the physical parameters required for APeCG from trajectory data. The human-driven vehicle trajectory datasets (HIGHSIM) were used to train the proposed PeMTFLN. The trajectories prediction experiments show that PeMTFLN exhibits superior compared to the baseline models in terms of predictive accuracy in speed and gap. The stability analysis result shows that the physical parameters in APeCG is able to reproduce the platoon stability in real-world condition. In simulation experiments, PeMTFLN performs low inference error in platoon trajectories generation. Moreover, PeMTFLN also accurately reproduces ground-truth safety statistics. The code of proposed PeMTFLN is open source.