Articles | Volume 24, issue 4
Nonlin. Processes Geophys., 24, 695–700, 2017
https://doi.org/10.5194/npg-24-695-2017
Nonlin. Processes Geophys., 24, 695–700, 2017
https://doi.org/10.5194/npg-24-695-2017

Brief communication 23 Nov 2017

Brief communication | 23 Nov 2017

Brief communication: Multiscaled solitary waves

Oleg G. Derzho 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.

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Short summary
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.