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Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation
The appearance and disappearance of short-lived large-amplitude pulses in a nonlinear long wave model is studied in the framework of the modified Korteweg-de Vries equation. The major mechanism of such wave generation is modulational instability leading to the generation and interaction of the breat...
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| Main Authors: | , , , , |
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| Format: | Default Preprint |
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2004
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| Online Access: | https://hdl.handle.net/2134/241 |
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| _version_ | 1822181559227121664 |
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| author | Roger Grimshaw Efim N. Pelinovsky Tatiana G. Talipova Michael Ruderman Robert Erdelyi |
| author_facet | Roger Grimshaw Efim N. Pelinovsky Tatiana G. Talipova Michael Ruderman Robert Erdelyi |
| author_sort | Roger Grimshaw (1258863) |
| collection | Figshare |
| description | The appearance and disappearance of short-lived large-amplitude pulses in a nonlinear long wave model is studied in the framework of the modified Korteweg-de Vries equation. The major mechanism of such wave generation is modulational instability leading to the generation and interaction of the breathers. The properties of breathers are studied both within the modified Korteweg -de Vries equation, and also within the nonlinear Schrödinger equation derived by an asymptotic reduction from the modified Korteweg -de Vries for weakly nonlinear wave packets, The associated spectral problems (AKNS or Zakharov-Shabat) of the inverse-scattering transform technique also utilized. Wave formation due to this modulational instability is investigated for localized and for periodic disturbances. Nonlinear-dispersive focusing is identified as a possible mechanism for the formation of anomalously large pulses. |
| format | Default Preprint |
| id | rr-article-9383876 |
| institution | Loughborough University |
| publishDate | 2004 |
| record_format | Figshare |
| spelling | rr-article-93838762004-01-01T00:00:00Z Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation Roger Grimshaw (1258863) Efim N. Pelinovsky (7159925) Tatiana G. Talipova (7159928) Michael Ruderman (7160645) Robert Erdelyi (7160648) Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified The appearance and disappearance of short-lived large-amplitude pulses in a nonlinear long wave model is studied in the framework of the modified Korteweg-de Vries equation. The major mechanism of such wave generation is modulational instability leading to the generation and interaction of the breathers. The properties of breathers are studied both within the modified Korteweg -de Vries equation, and also within the nonlinear Schrödinger equation derived by an asymptotic reduction from the modified Korteweg -de Vries for weakly nonlinear wave packets, The associated spectral problems (AKNS or Zakharov-Shabat) of the inverse-scattering transform technique also utilized. Wave formation due to this modulational instability is investigated for localized and for periodic disturbances. Nonlinear-dispersive focusing is identified as a possible mechanism for the formation of anomalously large pulses. 2004-01-01T00:00:00Z Text Preprint 2134/241 https://figshare.com/articles/preprint/Short-lived_large-amplitude_pulses_in_the_nonlinear_long-wave_model_described_by_the_modified_Korteweg_de_Vries_equation/9383876 CC BY-NC-ND 4.0 |
| spellingShingle | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified Roger Grimshaw Efim N. Pelinovsky Tatiana G. Talipova Michael Ruderman Robert Erdelyi Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation |
| title | Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation |
| title_full | Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation |
| title_fullStr | Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation |
| title_full_unstemmed | Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation |
| title_short | Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation |
| title_sort | short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified korteweg–de vries equation |
| topic | Other mathematical sciences not elsewhere classified untagged Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/241 |