Soliton dynamics in the rotation modified Benjamin-Ono equation

We study soliton formation and interaction in the non-integrable rotation-modified Benjamin–Ono (rmBO) equation with “anomalous” (positive) dispersion. This equation is applicable to the description of wave processes in plasma and possibly in other media. We show that specific solitons with zero total mass and non-monotonic asymptotics can emerge from pulse-type initial perturbations of a certain polarity. These solitons can form either regular trains ranked by amplitude, or irregular nonstationary configurations of bounded interacting solitons, or stationary moving multi-solitons. We further demonstrate that the interactions of solitons in the rmBO equation are inelastic, resulting in the emergence of a “soliton-champion” within closed systems. For instance, in systems with periodic boundary conditions, only the soliton with the greatest amplitude persists, effectively eliminating all other solitons after interacting with them. Solitons in the rmBO equation are rather robust; they gradually decay under the influence of weak dissipation, ordinarily radiating small-amplitude quasi-linear wave trains. We demonstrate this using the generalized rmBO equation augmented by a term responsible for Reynolds dissipation. In contrast, the influence of Rayleigh dissipation or Landau damping do not lead to wave train radiation in the process of soliton propagation and decay.