Formation of freak waves in a soliton gas described by the modified Korteweg–de Vries equation

Abstract

The nonlinear dynamics of multisoliton, differently polar fields is investigated within the framework of the modified Korteweg–de Vries equation. It is shown that the occurrence of abnormally large waves (freak waves) is possible in similar fields, which is associated with the modulation instability of cnoidal waves. The statistical moments of wave fields are investigated. It is shown that an increase in the coefficient of excess due to the interaction of solitons correlates with an increase in the probability of occurrence of freak waves. It is shown that the nonlinear interaction of differently polar solitons results in variation of the distribution functions of peak characteristics: the fraction of low-amplitude waves decreases, while that of the waves with large amplitudes increases. The dependence of the intensity of the density of the characteristics of the soliton gas is shown.