Brief communication: Multiscaled solitary waves

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.

Capillary-gravitational waves and storage of liquid CO2 in the oceans

“…Some solutions are entirely oscillatory without decay while others represent oscillatory decay [6]. The considered waves permit bore-like solutions and multiscaling [4,7] even for purely gravitational dispersion in the pseudo-integral form. Stability of stationary solutions for the derived equation is an important yet open question.…”