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On the Changing Wigner Stability of Ion Acoustic Soliton in a Four Component Incoherent Plasma and Akhmediev Breather

Chowdhury AR, Chaudhuri S, Chowdhury KR 

 We have analysed a situation on a four component incoherent plasma which shows interesting patterns in Wigner stability as the electron-ion temperature ratio (α) and the superthermal parameter (�?¸) is varied. The corresponding Nonlinear Schrödinger equation is deduced with the help of Krylov-Bogoliubov-Mitropolsky (KBM) approach. In the next stage we show how to take care of incoherence in the density profile with the help of dynamical equation for the correlation function <R(x,t)R(x’,t’)>with the help of Wigner-Moyal transform. It is observed that even this equation can be linearized to study the modulational stability which is actually Wigner Stability. An interesting and new feature is that when the ion-electron temperature ratio changes there is a change of stability. As such we get a switch-over from bright to dark soliton. A similar phenomenon is also seen to happen when the super-thermal parameter ‘�?¸’ changes. We have also seen that our NLS equation also support a very new kind of breather soliton known as Akhmediev breather.