Abstract: We derive a classical equation of motion on the superconducting phase in Josephson coupled layered High-Tc superconductors from the effective action obtained by using the path-integral method for the BCS microscopic theory considering the Josephson coupling between neighboring superconducting layers. The equation can describe the dynamics of the superconducting phase in the presence of the ab-plane parallel magnetic field. We perform numerical simulations on the equation, and study the dynamics of the superconducting phase under the collective motions of the Josephson vortices. In the simulations, we employ the open boundary condition in the 2D rectangular computational region, and measure the local electric field at the edge from interests about the emission of the electromagnetic wave by the flux flow. It is found that in the low field region, chaotic dynamics of the electric field is observed by reflecting non-regular motions of weakly correlated vortices. On the other hand, in the high field region, regular oscillations of the electric field can be detected as long as the stability of the driven vortex lattice is maintained, while further increasing the transport current results in instabilities of the driven vortex lattice and chaotic oscillations of the electric field appear. !18
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