Modelling train dynamics is essential for the platoon control of virtually coupled train sets (VCTS). Variable rail-wheel conditions and high data collection costs pose substantial challenges for both physics-based and data-driven models, especially when unit trains in the VCTS are heterogenous. This study introduces a train dynamics model that integrates parameter identification of basic resistance with physics-informed neural networks. The developed physics-informed neural network for train dynamics modelling (PINN-TDM) identifies key resistance parameters using the Davis formula. By combining the strengths of traditional modelling and data-driven approaches, the PINN-TDM provides accurate predictions of train dynamics, accommodating variations due to changes in rail-wheel conditions and heterogeneity among unit trains. Compared to conventional neural network models that lack physical guidance, the PINN-TDM demonstrates enhanced performance in data-limited conditions. Furthermore, this study incorporates the PINN-TDM into a model predictive control framework and derives the sufficient condition for heterogeneous string stability in the frequency domain using the Laplacian transformation. This enables the analysis of the impact of train dynamics heterogeneity on the stable region. Simulation experiments show that the integrated controller improves the precision of trajectory tracking and the stability of the VCTS under diverse rail-wheel conditions.