Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework
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 th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/9/1445 |
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| author | Ekaterina Didenkulova Efim Pelinovsky |
| author_facet | Ekaterina Didenkulova Efim Pelinovsky |
| author_sort | Ekaterina Didenkulova |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T16:38:08Z |
| format | Article |
| id | doaj.art-b943c673adf64c55a5130324cef81fee |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T16:38:08Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b943c673adf64c55a5130324cef81fee2023-11-20T12:15:54ZengMDPI AGSymmetry2073-89942020-09-01129144510.3390/sym12091445Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation FrameworkEkaterina Didenkulova0Efim Pelinovsky1Department of Information Systems, National Research University Higher School of Economics, 25/12, Bolshaya Pecherskaya Street, 603155 Nizhny Novgorod, RussiaDepartment of Information Systems, National Research University Higher School of Economics, 25/12, Bolshaya Pecherskaya Street, 603155 Nizhny Novgorod, RussiaPairwise 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.https://www.mdpi.com/2073-8994/12/9/1445breathersolitonmodified Korteweg–de Vries equationsoliton turbulencebreather turbulence |
| spellingShingle | Ekaterina Didenkulova Efim Pelinovsky Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework Symmetry breather soliton modified Korteweg–de Vries equation soliton turbulence breather turbulence |
| title | Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework |
| title_full | Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework |
| title_fullStr | Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework |
| title_full_unstemmed | Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework |
| title_short | Soliton–Breather Interaction: The Modified Korteweg–de Vries Equation Framework |
| title_sort | soliton breather interaction the modified korteweg de vries equation framework |
| topic | breather soliton modified Korteweg–de Vries equation soliton turbulence breather turbulence |
| url | https://www.mdpi.com/2073-8994/12/9/1445 |
| work_keys_str_mv | AT ekaterinadidenkulova solitonbreatherinteractionthemodifiedkortewegdevriesequationframework AT efimpelinovsky solitonbreatherinteractionthemodifiedkortewegdevriesequationframework |