On the dynamical stochastic electrostatic noise fluctuations in Zakharov model

Several of nonlinear plasma and burst electrostatic waves with vastly changing electric fields existed in a widely stochastic ranges in magnetosphere and space. According to the theory of stochastic-growth and density turbulence, it explained that the fluctuations, damping and electrostatic forcing produce in localized space regions. Theoretically, this plasma wave can be described by Schrödinger and Zakharov equations with stochastic term, which is applicable widely in plasma of space applications. Mathematical methods have been applied to produce new stochastic solutions for Zakharov model in subsonic limit with noises in Itô sense. The obtained solutions in the exact solitonic, breather envelopes structure, localized envelopes, dark dissipative blow-up wave, explosive, shocks and shock-like solitons becomes important in investigating electrostatic waves in aurora and solar–Wind. Finally, the effects of noise terms in Itô sense have been discussed and may be applicable to use in bursty waves in cusps regions and solar–wind.