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3-D nonlinear electrostatic plasma wave is periodic along its longitudinal direction. By strictly analyzing a universal equation set of charged particles system, we find that such a longitudinal periodicity has a severe constraint on the transverse shape of a 3-D electrostatic structure. Only few allowed transverse shapes could warrant the longitudinal periodicity. This longitudinal periodicity in real space shapes can lead to a corresponding periodic structure in phase space. PACS: 52.35.-g, 52.35.Fp, 52.35.Mw, 52.35.Sb, 52.65.-y.

Real Spatial Shapes and Phase Space Structures of 3-D Nonlinear Electrostatic Plasma Wave