Envelope solitons in a weakly magnetized electron-positron plasma with relativistic temperature F. A. Asenjo 1 , F. A. Borotto 2 , A. C.-L. Chian 3,4,5 , V. Muñoz 6 , J. A. Valdivia 6,7 and E. Rempel, 5,8 1 Institute for Fusion Studies, The University of Texas at Austin, USA 2 Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Chile 3 Observatoire de Paris, LESIA, CNRS, France 4 National Institute for Space Research (INPE), Brazil 5 World Institute for Space Environment Research (WISER), Brazil 6 Departamento de Física, Facultad de Ciencias, Universidad de Chile, Chile 7 Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA 8 Institute of Aeronautical Technology (ITA), Brazil Introduction The self-modulation of a relativistic nonlinear circularly (and linearly) polarized electromag- netic wave in an electron-positron plasma was first investigated by Chian and Kennel [1] in the cold unmagnetized case. A large number of papers have improved the original model by Chian and Kennel [1], including the existence of Alfvén vortices in the presence of a strong magnetic field, the influence of a strong magnetic field and ions, and the effects of relativistic temperatures and phonon damping. In this work we follow this research subject, by studying the self-modulation of a nonlin- ear circularly polarized electromagnetic wave in a weakly magnetized relativistic hot electron- positron plasma. [2] Relativistic plasmas with a finite temperature It is possible to formulate a theory for hot relativistic plasmas in a covariant form [3] where the fluid and the electromagnetic fields are unified into a single field. The plasma dynamics is given by Maxwell’s equations, the continuity and the motion equations for each fluid: ∂ ∂ t ( n j γ j ) +  ∇ · ( n j γ j  v j ) = 0 , (1)  ∂ ∂ t + v j ·  ∇  ( f j γ j  v j ) = q j m   E +  v j c ×  B  − 1 n j mγ j  ∇ p j , (2) where  v j ,γ j , q j , p j and n j are the velocity, relativistic Lorentz factor, charge, pressure and rest- frame number density of each fluid, respectively, m is the electron mass, c is the speed of light, and  E and  B are the electric and magnetic fields. 39 th EPS Conference & 16 th Int. Congress on Plasma Physics P2.174