AbstractThree Coupled nonlinear Schrödinger equations for two transverse and one longitudinal waves has been derived. These equations have been derived using two space time scale techniques. It is shown that even without the effect of relativistic mass variation and ion contribution, all three waves may propagate in the form of localized solitary envelope with a common velocity for small values of the transverse wave numbers and the longitudinal wave number far exceedingkD√me/mi. Stability analysis of the localized solitary wave form reveals that these wave forms are stab