Abstract
Association between weakly relativistic ion modulation modes described by the Korteweg–de Vries equation in the small wavenumber region and by the nonlinear Schrödinger equation in the finite wavenumber region is found in a collisionless unmagnetized plasma. It is shown that the stability criterion for the modulation of the ion wave envelope depends on the relativistic effect. The present results may explain the observations obtained in space plasmas.