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A classical fluid description is used to investigate nonlinear interactions between an electron-type neutrino beam and a relativistic collisionless unmagnetized electron-positron plasma. It is shown that during the interaction a large amplitude wakefield plasma wave is generated in such a way that charged particles trapped in this wave can be accelerated to high energies. It is also shown that the symmetry among the electron and positron dynamics is broken in the presence of intense neutrino bursts.