Characteristics of soliton gas with the strongest pairwise soliton interactions in the focusing Gardner equation

For the focusing Gardner equation, we investigate the dynamics of soliton gas (SG) incorporating the strongest pairwise soliton interactions that achieve the maximum attainable amplification AI=2$$AI = 2$$. In our simulated SG, the interactions of positive solitons overtaking negative ones are dominant because the velocities of most of positive solitons are larger than those of negative ones in the initial distribution. As the number of bipolar soliton pairs with AI=2$$AI = 2$$ increases, the third moment decrease in absolute while the fourth moment increases. Meanwhile, the maximum values in the global wave field increase significantly while the minimum values exhibit a relatively modest increase, owing to the generation of many high positive transient waves during interactions, as compared to the limited production of high negative transient waves. Also, an obvious elevation in the tails of global probability density functions is observed for positive wave amplitudes, which indicates an increase of the number of rogue wave (RW) events in the wave field. In addition, the RW occurrence probability does not increase but rather decreases, in contrast to the properties of the integrable turbulence driven by modulation instability. Our findings may be useful for realizing some controllable experiments of the SGs in water waves.