Abstract
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.
Reference16 articles.
1. Benjamin, T. B.: A new kind of solitary wave, J. Fluid Mech., 245, 401–403, 1992.
2. Benney, D. G. and Ko, D. R. S.: The propagation of long large amplitude internal waves, Stud. Appl. Math., 59, 187–195, 1978.
3. Bona, J. L., Souganidis, P. E., and Strauss, W. A.: Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Roy. Soc. London Ser. A, 411, 395–412, 1987.
4. Derzho, O. G. and Borisov, A. A.: The structure of steady state solitary waves of finite amplitude, Izv. Akad. Nauk SSSR, Ser. Tekh. Nauk, 2, 60–70, 1990 (in Russian).
5. Derzho, O. G. and Grimshaw, R.: Solitary waves with a vortex core in a shallow layer of stratified fluid, Phys. Fluids, 9, 3378–3385, 1997.
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