Brief communication: Multiscaled solitary waves
It is analytically shown how competing nonlinearities yield multiscaled structures for internal solitary waves in stratified shallow fluids. These solitary waves only exist for large amplitudes beyond the limit of applicability of the Korteweg–de Vries (KdV) equation or its usual extensions. The...
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2017-11-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://www.nonlin-processes-geophys.net/24/695/2017/npg-24-695-2017.pdf |
| Summary: | It is analytically shown how competing nonlinearities yield multiscaled
structures for internal solitary waves in stratified shallow fluids. These
solitary waves only exist for large amplitudes beyond the limit of
applicability of the Korteweg–de Vries (KdV) equation or its usual
extensions. The multiscaling phenomenon exists or does not exist for almost
identical density profiles. The trapped core inside the wave prevents the
appearance of such multiple scales within the core area. The structural
stability of waves of large amplitudes is briefly discussed. Waves of large
amplitudes displaying quadratic, cubic and higher-order nonlinear terms have
stable and unstable branches. Multiscaled waves without a vortex core are
shown to be structurally unstable. It is anticipated that multiscaling
phenomena will exist for solitary waves in various physical contexts. |
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| ISSN: | 1023-5809 1607-7946 |