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Nonlin. Processes Geophys., 24, 695-700, 2017
https://doi.org/10.5194/npg-24-695-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Brief communication
23 Nov 2017
Brief communication: Multiscaled solitary waves
Oleg G. Derzho Institute of Thermophysics, Russian Academy of Sciences, Novosibirsk, Russia
Abstract. 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.

Citation: Derzho, O. G.: Brief communication: Multiscaled solitary waves, Nonlin. Processes Geophys., 24, 695-700, https://doi.org/10.5194/npg-24-695-2017, 2017.
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It is analytically shown how competing nonlinearities yield multiscaled structures for internal solitary waves in stratified fluids. These solitary waves only exist for large amplitudes beyond the limit of applicability of the KdV/mKdV equations. Multiscaled waves without vortex cores are shown to be structurally unstable. It is anticipated that multiscaling phenomena will exist for solitary waves in various physical contexts.
It is analytically shown how competing nonlinearities yield multiscaled structures for internal...
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