On the collision of railcars as an interaction of nonlinear shock wave-like perturbations

Abstract

The article examines the collision of railcars based on the solution of hydrodynamic equations using shock waves during the transition from weak nonlinearity to perturbations of arbitrary amplitude. Several new mathematical issues have been set for the development of high-speed transport, which can be solved in the framework of hydrodynamics to describe the process of hydrodynamics, creating effective rolling stock dampers. which requires the improvement and development of the corresponding mathematical apparatus. In this work, we use a hydrodynamic approach to find the density distributions of matter during railcar collisions at high speeds, which is important in light of the problems of high-speed transport. In our approach, we found an analytical solution to the obtained hydrodynamic equations for the one-dimensional case. The equations under study were obtained taking into account nonequilibrium processes. To find a solution to the hydrodynamic equations, the shock wave approximation is used, similar to the soliton solutions we considered earlier. Taking into account possible deviations from the results of a one-dimensional problem is considered. Such a reduction of solutions of hydrodynamic equations to shock waves has not been considered previously and may be of interest for a wide variety of applied problems. The resulting consideration of railcar collisions is important for solving problems of transport safety and technospheric safety.