Relativistic charge solitons created due to non-linear Landau damping: a candidate for explaining coherent radio emission in pulsars

A potential resolution for the generation of coherent radio emission in pulsar plasma is the existence of relativistic charge solitons, which are solutions of non-linear Schrödinger equation (NLSE). In an earlier study, Melikidze et al. investigated the nature of these charge solitons; however, their analysis ignored the effect of non-linear Landau damping, which is inherent in the derivation of the NLSE in the pulsar pair plasma. In this paper we include the effect of non-linear Landau damping and obtain solutions of the NLSE by applying a suitable numerical scheme. We find that for reasonable parameters of the cubic non-linearity and non-linear Landau damping, soliton-like intense pulses emerge from an initial disordered state of Langmuir waves and subsequently propagate stably over sufficiently long times, during which they are capable of exciting the coherent curvature radiation in pulsars. We emphasize that this emergence of stable intense solitons from a disordered state does not occur in a purely cubic NLSE; thus, it is caused by the non-linear Landau damping.