On the envelope soliton near critical density in a plasma with cold ions and two-temperature electrons

Summary We have analysed the formation of envelope soliton near critical density in a plasma consisting of two-temperature electrons and cold ions. The non-linear Schr?dinger-like equation obtained isiφ _t +pφ _xx +q|φ|⁴φ=0 which we call the modified non-linear Schr?dinger equation. It is also observed that this approach leads to a physical situation where a linear combination of both the modified and usual NLS equations holds, in the formiφ _t +pφ _xx +q ₁|φ|²φ +q ₂|φ|⁴φ=0. It is demonstrated through graphical analysis thatq ₁,q ₂, thought of as a function of β(=T _el/T _eh), behave in opposite way. That is, whenq ₁ grows,q ₂ decays, or vice versa. Lastly we demonstrate that this equation can sustain a type of solution other than the usual solitary profile. The form of such a wave is also depicted graphically.