Articles | Volume 24, issue 4
Brief communication
23 Nov 2017
Brief communication |  | 23 Nov 2017

Brief communication: Multiscaled solitary waves

Oleg G. Derzho

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Subject: Nonlinear Waves, Pattern Formation, Turbulence | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
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Cited articles

Benjamin, T. B.: A new kind of solitary wave, J. Fluid Mech., 245, 401–403, 1992.
Benney, D. G. and Ko, D. R. S.: The propagation of long large amplitude internal waves, Stud. Appl. Math., 59, 187–195, 1978.
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.
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).
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.
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.