The simplest zero approximation of the description of the dynamics of a rod system is considered, taking into account the mutual influence of the nearest neighbours. Within the approximation, the behaviour of each rod is described by a 1D/2D oscillator model. For the 1D system, the Toda potential and its extension to the 2D case are accounted. From the point of view of reactor stability analysis, the presence of soliton-type solutions is of interest. The system dynamics is considered within Hamilton’s formalism.

Numerical modelling with various initial conditions and interaction potentials is performed. The procedure for finding the natural frequencies of the system is described, and an analysis of symmetry groups in phase space is given.