Nonlinear dynamics of a soliton gas: Modified Korteweg–de Vries equation framework

• The dynamics of multi-soliton field within the framework of the modified Korteweg–de Vries equation is considered.
• It is shown that nonlinear interaction modifies the distribution function of the wave amplitudes and statistical moments.
• It is demonstrated that freak waves can appear in a bipolar soliton gas.

Dynamics of random multi-soliton fields within the framework of the modified Korteweg–de Vries equation is considered. Statistical characteristics of a soliton gas (distribution functions and moments) are calculated. It is demonstrated that the results sufficiently depend on the soliton gas properties, i.e., whether it is unipolar or bipolar. It is shown that the properties of a unipolar gas are qualitatively similar to the properties of a KdV gas [Dutykh and Pelinovsky (2014) [1]]: nonlinear interaction leads to an increase in the part of small-amplitude waves and decrease in the third and fourth statistical moments. The dynamics of bipolar soliton fields is more interesting. In this case, kurtosis (the fourth moment) and the part of large-amplitude waves increase during the interaction. It is demonstrated that the freak wave appearance in a soliton gas is possible due to the attraction of large bipolar solitons.