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

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.

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References in corpus (5)

• Kinetic equation for a dense soliton gas
• Numerical simulation of a solitonic gas in KdV and KdV-BBM equations
• Statistical Description of Acoustic Turbulence
• Interaction properties of complex mKdV solitons
• Geometric numerical schemes for the KdV equation

Cited by in corpus (4)

• The role of multiple soliton and breather interactions in generation of rogue waves: the mKdV framework
• Investigating overtaking collisions of solitary waves in the Schamel equation
• Stability and interaction of compactons in the sublinear KdV equation
• Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions