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

Physical Review Letters. 2016. Vol. 117. No. 21. P. 214501.

Pelinovsky E., Slunyaev A. V.

The role of multiple soliton and breather interactions in the formation of very high waves is disclosed
within the framework of the integrable modified Korteweg–de Vries (MKdV) equation. Optimal conditions
for the focusing of many solitons are formulated explicitly. Namely, trains of ordered solitons with alternate
polarities evolve to huge strongly localized transient waves. The focused wave amplitude is exactly the sum
of the focusing soliton heights; the maximum wave inherits the polarity of the fastest soliton in the train.
The focusing of several solitary waves or/and breathers may naturally occur in a soliton gas and will lead to
rogue-wave-type dynamics; hence, it represents a new nonlinear mechanism of rogue wave generation. The
discovered scenario depends crucially on the soliton polarities (phases), and is not taken into account by
existing kinetic theories. The performance of the soliton mechanism of rogue wave generation is shown for
the example of the focusing MKdV equation, when solitons possess “frozen” phases (certain polarities),
though the approach is efficient in some other integrable systems which admit soliton and breather
solutions.

Priority areas:
mathematics

Language:
English

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Зайцев В. И., Щавелин В. М., М. : ВИНИТИ РАН, 1985

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Teichmüller theory is a ramified and rapidly developing area of mathematics which has multiple connections with other directions in the mathematical sciences and with their applications, first and foremost in mathematical physics. In this survey the main lines of development of this theory and its applications to string theory are presented in a historical context.
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Theoretical models of the conformational behavior of flexible polymer chains in mixed solvents enunciated in the world literature during the last decade are critically reviewed. Models describing different mechanisms of coil-to-globule transitions in a good solvent induced by cosolvent addition are highlighted. Special attention is given to the analysis of theoretical approaches to describing the ...

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Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...

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