A solution for the phase-lip-center (PSC), arising from different winding rates of the charge-density-wave (CDW) phase is found from the microscopic theory. The PSC has a form of a dynamic amplitude soliton with oscillating energy level. Outside the PSC the phase is governed by the diffusion equation, which takes into account the screening of the deformed CDW by quasiparticles. Near the PSC the conductivity oscillates because of the oscillations of the quasiparticle density.
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