The generation of nonlinear harmonics by a self-acting dipole pulse of electromagnetic field evolving in a vacuum is considered. Using Maxwell nonlinear equations obtained from the Heisenberg-Euler Lagrangian, it is shown that in the first order of perturbation theory the generation of the third harmonic does not occur, as follows from the law of conservation of energy-momentum. It is demonstrated that accounting for nonlinear effects leads to the generation of an octupole electromagnetic pulse at the frequency of the initial dipole pulse. Using numerical simulations the spectrum of the generated radiation for a Gaussian initial dipole pulse was obtained and it was shown that its maximum is shifted in direction of larger frequencies. Keywords: nonlinear electrodynamics, conservation of energy-momentum, Heisenberg-Euler Lagrangian, radiation.