Equations for Deep Water Counter Streaming Waves and New Integrals of Motion
The waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The fundamental...
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MDPI AG
2019-03-01
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| Series: | Fluids |
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| Online Access: | http://www.mdpi.com/2311-5521/4/1/47 |
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doaj-5099daee1bc147ce9d6e239b4b0004852020-11-25T01:21:19ZengMDPI AGFluids2311-55212019-03-01414710.3390/fluids4010047fluids4010047Equations for Deep Water Counter Streaming Waves and New Integrals of MotionAlexander Dyachenko0Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region 142432, RussiaThe waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The fundamental consequence of this decomposition is the conservation of the “number of waves” in each particular group. The envelope approximation for the waves in each group of counter streaming waves is obtained.http://www.mdpi.com/2311-5521/4/1/47water wavesintegrals of motionHamiltonian formalismcanonical transformationNLSE approximation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alexander Dyachenko |
| spellingShingle |
Alexander Dyachenko Equations for Deep Water Counter Streaming Waves and New Integrals of Motion Fluids water waves integrals of motion Hamiltonian formalism canonical transformation NLSE approximation |
| author_facet |
Alexander Dyachenko |
| author_sort |
Alexander Dyachenko |
| title |
Equations for Deep Water Counter Streaming Waves and New Integrals of Motion |
| title_short |
Equations for Deep Water Counter Streaming Waves and New Integrals of Motion |
| title_full |
Equations for Deep Water Counter Streaming Waves and New Integrals of Motion |
| title_fullStr |
Equations for Deep Water Counter Streaming Waves and New Integrals of Motion |
| title_full_unstemmed |
Equations for Deep Water Counter Streaming Waves and New Integrals of Motion |
| title_sort |
equations for deep water counter streaming waves and new integrals of motion |
| publisher |
MDPI AG |
| series |
Fluids |
| issn |
2311-5521 |
| publishDate |
2019-03-01 |
| description |
The waves on a free surface of 2D deep water can be split into two groups: the waves moving to the right, and the waves moving to the left. A specific feature of the four-wave interactions of water waves allows to describe the evolution of the two groups as a system of two equations. The fundamental consequence of this decomposition is the conservation of the “number of waves” in each particular group. The envelope approximation for the waves in each group of counter streaming waves is obtained. |
| topic |
water waves integrals of motion Hamiltonian formalism canonical transformation NLSE approximation |
| url |
http://www.mdpi.com/2311-5521/4/1/47 |
| work_keys_str_mv |
AT alexanderdyachenko equationsfordeepwatercounterstreamingwavesandnewintegralsofmotion |
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