V.I. Erofeyev, A.O. Malkhanov

The propagation of longitudinal wave in a homogeneous nonlinear superconducting rod has been investigated. The rod has been placed in external magnetic field. The nonlinear Bernoulli model has been used for describing longitudinal oscillations of the rod. The system which explain the evolution of magnetic and deformation fields taking into account their influence on each other calls the system of magnetoelasticity equations. In this case it is unable to get the precise analytical solution for that system. That is why the method of small parameter has been used. This method allows to study successive approximations of initial system. In the first approximation the initial system can be transformed to Riemann equation. Profile of the Riemann wave is corrupting along with propagation because different wave-s pieces have different velocity. That is why at a certain moment of time the wave is turning over. Under this model the time when the wave turns over depends on the value of the external magnetic field. The profile of the wave has been taken as a sine at initial moment of time. The moment of the wave-s inversion grows with increasing of the value of the external magnetic field. Thereby external magnetic field stabilizes the Riemann wave increasing the time of its inversion.