Two-soliton interaction in the framework of modified Korteweg - de Vries equation

TL;DR

This paper investigates the interaction of two solitons with different polarities in the modified Korteweg-de Vries equation, analyzing their effects on wave field moments and turbulence characteristics.

Contribution

It provides a detailed analysis of two-soliton interactions in the mKdV framework, highlighting differences from KdV interactions and implications for turbulence theory.

Findings

Same polarity soliton interactions reduce skewness and kurtosis.

Different polarity soliton interactions increase skewness and kurtosis.

Results differ from KdV soliton interaction estimations.

Abstract

Interaction of two solitons of the different polarities in the framework of modified Korteweg-de Vries (mKdV) equation is studied. Three types of soliton interaction are considered: exchange and overtaking for solitons of the same polarity, and absorb-emit for solitons of different polarity. Features of soliton interaction are studied in details. Since the interaction of solitons is an elementary act of soliton turbulence, the moments of the wave field up to fourth are studied, which are usually considered in the turbulence theory. It is shown that in the case of interaction of solitons of the same polarity the third and fourth moments of the wave field, which determine the coefficients of skewness and kurtosis in the theory of turbulence, are reduced, while in the case of interaction of solitons of different polarity these moments are increased. The results are compared with the estimations for the two-soliton interaction in the framework of the Korteweg - de Vries (KdV) equation.