Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework

Symmetry

Ekaterina Didenkulova¹  Efim Pelinovsky¹ 

[1] Department of Information Systems, National Research University Higher School of Economics, 25/12, Bolshaya Pecherskaya Street, 603155 Nizhny Novgorod, Russia;

关键词: breather;    soliton;    modified Korteweg–de Vries equation;    soliton turbulence;    breather turbulence;   

DOI  :  10.3390/sym12091445

来源: DOAJ

【 摘 要 】

Pairwise interactions of particle-like waves (such as solitons and breathers) are important elementary processes that play a key role in the formation of the rarefied soliton gas statistics. Such waves appear in different physical systems such as deep water, shallow water waves, internal waves in the stratified ocean, and optical fibers. We study the features of different regimes of collisions between a soliton and a breather in the framework of the focusing modified Korteweg–de Vries equation, where cubic nonlinearity is essential. The relative phase of these structures is an important parameter determining the dynamics of soliton–breather collisions. Two series of experiments with different values of the breather’s and soliton’s relative phases were conducted. The waves’ amplitudes resulting from the interaction of coherent structures depending on their relative phase at the moment of collision were analyzed. Wave field moments, which play a decisive role in the statistics of soliton gases, were determined.

【 授权许可】

Unknown