Characteristic behaviour of N-order ion acoustic rogue waves solution in electron-positron-ion plasmas

Abstract

The characteristic behaviour of breathers as well as N-order Rogue wave (RW) solution in homogeneous unmagnetized electron-positron-ion plasmas (consisting of cold ions, and isothermal Maxwellian electrons and positrons) has been studied theoretically. Nonlinear Schrödinger (NLS) equation is derived employing Krylov-Bogoliubov-Mitropolosky (KBM) perturbation technique in solving the concerned problems. The analytical solution of the NLS equation in the forms of breathers such as Akhmediev breather (AB), Kuznetsov-Ma breather (KM) solitons, as well as first-, second-, third-, and fourth-order RWs solution are obtained. The characteristic behaviour of breathers’ and their dependency on the relevant physical parameters are examined. The different orders of RWs are analyzed to obtain the region of existence of ion acoustic (IA) rogue waves (IARWs) with respect to unstable region. The potential profiles concerning different orders of RWs depend on the ratio of positron to electron concentrations ( ρ ) and wave number ( k ). Analysis reveals that the spatial difference between the two adjacent peaks of AB profiles are increasing with the enhancement of transformer physical parameter ( Λ ), while the temporal evolution between the two neighboring peaks of KM profiles decreases with increasing Λ and the amplitudes become large as well. The amplitudes of first-, second-, and third-order RWs profiles are decreasing with increasing ρ while the amplitude of fourth-order RWs profile is increasing. The results obtained in this study may be useful in understanding the propagation of nonlinear waves in optical fibers, Bose-Einstein condensates, plasma physics and atmospheric physics.