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We study analytically and numerically how the radiation emitted by fundamental solitons in the form of dispersive waves is affected by the third and fourth-order dispersions when a higher-order soliton undergoes the fission process inside an optical fiber. Our results show that two dispersive wave sidebands appear in the output spectrum on opposite sides of the input spectrum. The frequencies of these sidebands are set by the relative magnitudes of the third- and fourth-order dispersion parameters, but are not affected much by the Raman process. A well defined phase-matching condition accurately predicts these conjugate frequencies of dispersive wave. The relative amplitudes of these two sidebands are not equal because of the asymmetry induced by the third-order dispersion and higher-order nonlinearities. It is found that with increasing fourth-order dispersion the amplitude of both spectral components …