Stability of nonlinear stationary waves in composite superconductors

The thermomagnetic instability of the critical state in superconductors is analysed with account of the dissipation and dispersion. The possibility is demonstrated of the existance of a nonlinear shok wave describing the final stage of the instability evolution in a superconductor. The structures possess a finite-amplitude and propagate at a constant velocity. The apperance of these structures is qualititively described and the wave propagation velocity is estimated. The problem of nonlinear wave stability with respect to small thermal and electromagnetic perturbations. It is shown that only damped perturbations correspond to space-limited solutions.