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Observations suggest that coherent radio emission from pulsars is excited ina dense pulsar plasma by curvature radiation from charge bunches. Numerousstudies propose that these charge bunches are relativistic charge solitonswhich are solutions of the non-linear Schr\"{o}dinger equation (NLSE) with agroup velocity dispersion ($G$), cubic-nonlinearity($q$) and non-linear Landaudamping ($s$). The formation of stable solitons crucially depends on theparameters $G, q$ and $s$ and the particle distribution function. In this work,we use realistic pulsar plasma parameters obtained from observationalconstraints to explore the parameter space of NLSE for two representativedistribution functions (DF) of particles' momenta: Lorentzian (long-tailed) andGaussian (short-tailed). The choice of DF critically affects the value of$|s/q|$, which, in turn, determines whether solitons can form. Numericalsimulations show that well-formed solitons are obtained only for small valuesof $|s/q| \lesssim 0.1$ while for moderate and higher values of $|s/q| \gtrsim0.5$ soliton formation is suppressed. Small values for $|s/q| \sim 0.1$ arereadily obtained for long-tailed DF for a wide range of plasma temperatures. Onthe other hand, short-tailed DF provides these values only for some narrowrange of plasma parameters. Thus, the presence of a prominent high-energy tailin the particle DF favours soliton formation for a wide range of plasmaparameters. Besides pair plasma, we also include an iron ion component and findthat they make a negligible contribution in either modifying the NLSEcoefficients or contributing to charge separation.

Pulsar radio emission mechanism II. On the origin of relativistic Langmuir solitons in pulsar plasma