Modulational instability and on the existence of rogue wave in electron-ion-positron plasma with kappa distributed electrons

Modulational instability of ion-acoustic wave in an electron-ion-positron plasma is analyzed when the electrons are kappa distributed. Instead of the age old method of reductive perturbation technique we have followed a different methodology put forward by Zakharov, Karpman, Fried and Ichikawa. In this approach the stress is more on physics than the formalism. The nonlinear Schrodinger equation is derived and its two kinds of solution are obtained- Envelope Soliton and Rational Soliton. The stability criteria are established and studied by varying the positron density, temperature and wave number. Over and above we have found both dark- soliton and bright- soliton. An important feature of this method is that we can proceed to the critical case in a much simpler way. It may be added that the rational soliton is not a rogon, but a different form of nonlinear excitation for those values of plasma parameters for which we could test stability.