Hamiltonian description of wave dynamics in nonequilibrium media
We consider Hamiltonian description of weakly nonlinear wave dynamics in unstable and nonequilibrium media. We construct the appropriate canonical variables in the whole wavenumber space. The essentially new element is the construction of canonical variables in a vicinity of marginally stable points...
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| Format: | Article |
| Language: | English |
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Copernicus Publications
1994-01-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | http://www.nonlin-processes-geophys.net/1/234/1994/npg-1-234-1994.pdf |
| _version_ | 1828305413448138752 |
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| author | N. N. Romanova |
| author_facet | N. N. Romanova |
| author_sort | N. N. Romanova |
| collection | DOAJ |
| description | We consider Hamiltonian description of weakly nonlinear wave dynamics in unstable and nonequilibrium media. We construct the appropriate canonical variables in the whole wavenumber space. The essentially new element is the construction of canonical variables in a vicinity of marginally stable points where two normal modes coalesce. The commonly used normal variables are not appropriate in this domain. The mater is that the approximation of weak nonlinearity breaks down when the dynamical system is written in terms of these variables. In this case we introduce the canonical variables based on the linear combination of modes belonging to the two different branches of dispersion curve. <br> As an example of one of the possible applications of presented results the evolution equations for weakly nonlinear wave packets in the marginally stable area are derived. These equations cannot be derived if we deal with the commonly used normal variables. |
| first_indexed | 2024-04-13T14:29:13Z |
| format | Article |
| id | doaj.art-229e0b50116e4cc28cd5e47f3d44923c |
| institution | Directory Open Access Journal |
| issn | 1023-5809 1607-7946 |
| language | English |
| last_indexed | 2024-04-13T14:29:13Z |
| publishDate | 1994-01-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Nonlinear Processes in Geophysics |
| spelling | doaj.art-229e0b50116e4cc28cd5e47f3d44923c2022-12-22T02:43:14ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79461994-01-0114234248Hamiltonian description of wave dynamics in nonequilibrium mediaN. N. RomanovaWe consider Hamiltonian description of weakly nonlinear wave dynamics in unstable and nonequilibrium media. We construct the appropriate canonical variables in the whole wavenumber space. The essentially new element is the construction of canonical variables in a vicinity of marginally stable points where two normal modes coalesce. The commonly used normal variables are not appropriate in this domain. The mater is that the approximation of weak nonlinearity breaks down when the dynamical system is written in terms of these variables. In this case we introduce the canonical variables based on the linear combination of modes belonging to the two different branches of dispersion curve. <br> As an example of one of the possible applications of presented results the evolution equations for weakly nonlinear wave packets in the marginally stable area are derived. These equations cannot be derived if we deal with the commonly used normal variables.http://www.nonlin-processes-geophys.net/1/234/1994/npg-1-234-1994.pdf |
| spellingShingle | N. N. Romanova Hamiltonian description of wave dynamics in nonequilibrium media Nonlinear Processes in Geophysics |
| title | Hamiltonian description of wave dynamics in nonequilibrium media |
| title_full | Hamiltonian description of wave dynamics in nonequilibrium media |
| title_fullStr | Hamiltonian description of wave dynamics in nonequilibrium media |
| title_full_unstemmed | Hamiltonian description of wave dynamics in nonequilibrium media |
| title_short | Hamiltonian description of wave dynamics in nonequilibrium media |
| title_sort | hamiltonian description of wave dynamics in nonequilibrium media |
| url | http://www.nonlin-processes-geophys.net/1/234/1994/npg-1-234-1994.pdf |
| work_keys_str_mv | AT nnromanova hamiltoniandescriptionofwavedynamicsinnonequilibriummedia |