Two-Soliton Interaction Within the Framework of the Modified Korteweg-de Vries Equation

We study interaction of two solitons of different polarities within the framework of the modified Korteweg-de Vries equation. Three types of soliton interaction are considered, namely, exchange and overtaking interactions (for positive solitons) and an absorb-emit interaction (for solitons of different polarities). The soliton-interaction features are studied in detail. Since the soliton interaction is an elementary soliton-turbulence act, the wave-field moments from the first to the fourth inclusively, which are usually considered in the theory of turbulence, are studied. It is shown that during interaction of solitons of the same polarity, the third and fourth wave-field moments, which determine the skewness and kurtosis coefficients in the theory of turbulence, decrease, whereas for solitons of different polarities, these moments increase. The obtained results are compared with the estimates of two-soliton interaction within the framework of the Korteweg-de Vries equation.