The damping rates of edge magnetoplasmon (EMP) resonances in a two-dimensional electron system formed on a liquid-helium surface were measured at temperatures below 1.1K and in perpendicular magnetic fields up to 6T. By lowering the lateral confinement electric-field strength, we observed a clear evidence for an oscillation mode transformation from the conventional EMP into the coupled mode of EMP with the bounary displacement wave (BDW). It was found that the coupled BDW-EMP mode is characterized by strong damping. The damping rate enhancement in the coupled BDW-EMP mode is a manifestation of the incompressible motion of the classical electron liquid arising from strong electron correlation.
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