A coupled pair of nonlinear equations for the amplitude modulated Langmuir wave and the associated low frequency electric potential wave have been derived by relaxing quasineutrality condition of the frequency motion. Solitary wave solutions exist. It is found that the small correction term due to ion pressure changes the amplitude of the solitary wave.
1: IntroductionZAKHAROV equations [l] describe the interaction of high frequency Langmuir waves with low frequency plasma density fluctuations. The coupling between the high and low frequency oscillations arise through the ponderomotive force. The low frequency ion wave equation is derived from the' linear response of the low frequency motion. The charge neutrality is assumed for the low frequency part of the ion motion. Solitary wave solutions exist for these equations. If the soliton velocity tends toward the ionsound velocity the response time of the ion motions is increasingly important to the nature of the Langmuir solitons and the ZAKHAROV equations break down [2]. Therofore the nonlinearity of ion dynamics plays a vital roll in this case. I n experiments [3, 41 density depression of more than 10% have been observed. It was shown that nonlinearity of ion motion must be taken into account when the group velocity of the Langmuir wave is equal to the group velocity of ion acoustic waves taking the latter's dispersion into account [5, 61. I n this case the propagations of the two interacting waves -the Langmuir wave and the ion acoustic wave are described by a pair of coupled nonlinear Schrodinger equations. If the velocity of the plasma density is sufficiently closed to the ion sound velocity then, in some cases, the governing equations of motions are nonlinear Schrodinger equation describing the Langmuir wave is coupled to Korteweg-de Vries (KdV) or Boussinesq type equation [7-91. In this case the density cavity is sufficient to trap two solitons. The problem of transition from trapping of one soliton to trapping of two solitons was investigated by RAO and VERMA [lo] relaxing the quasineutrality condition of the low frequency motion.I n this paper we consider two fluid model hydrodynamic together with Poisson's equations where small effect due to ion pressure has been introduced. The problem is different from that of RAO and VERMA [lo] due to the count of the later effect. We have also concentrated our attention where the low frequen.cy potential is of the order of the square of the magnitude of the high frequency Langmuir field. We have also assumed that the ion acoustic wave phase velocity is much smaller than the electron thermal 1 Contrib. Plasma Phya. 29 (1989) 2