The role of multiple soliton and breather interactions in generation of rogue waves: the mKdV framework

摘要

The role of multiple soliton and breather interactions in formation of veryhigh waves is disclosed within the framework of integrable modified Korteweg -de Vries (mKdV) equation. Optimal conditions for the focusing of many solitonsare formulated explicitly. Namely, trains of ordered solitons with alternatepolarities evolve to huge strongly localized transient waves. The focused waveamplitude is exactly the sum of the focusing soliton heights; the maximum waveinherits the polarity of the fastest soliton in the train. The focusing ofseveral solitary waves or/and breathers may naturally occur in a soliton gasand will lead to rogue-wave-type dynamics; hence it represents a new nonlinearmechanism of rogue wave generation. The discovered scenario depends cruciallyon the soliton polarities (phases), and thus cannot be taken into account byexisting kinetic theories. The performance of the soliton mechanism of roguewave generation is shown for the example of focusing mKdV equation, whensolitons possess 'frozen' phases (polarities), though the approach works inother integrable systems which admit soliton and breather solutions.