Three dimensional (3D) relativistic electromagnetic sub-cycle solitons were observed in 3D Particle-in-Cell simulations of an intense short laser pulse propagation in an underdense plasma. Their structure resembles that of an oscillating electric dipole with a poloidal electric field and a toroidal magnetic field that oscillate in-phase with the electron density with frequency below the Langmuir frequency. On the ion time scale the soliton undergoes a Coulomb explosion of its core, resulting in ion acceleration, and then evolves into a slowly expanding quasi-neutral cavity.
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