1998/11/01 by A. Ludu, Andrei Ludu, Jerry P. Draayer +1 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Fluid Dynamics and Thin Films #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #nlin.PS #physics.atm-clus #physics.flu-dyn
paper · pdf · doi:10.1016/s0167-2789(98)00113-4
published as Physica D {\bf 123} (1998) 82 · 14 pages RevTex, 5 figures in ps
openalex publication_date 1998/11/01 · arxiv created 2000/03/26 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Localized patterns and nonlinear oscillation formation on the bounded free surface of an ideal incompressible liquid are analytically investigated . Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discused. A finite-difference differential generalized Korteweg-de Vries equation is shown to describe the three-dimensional motion of the fluid surface and the limit of long and shallow channels one reobtains the well known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial condition is introduced on a graphical-algebraic basis. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear physics since, up to an overall scale, these systems display liquid free surface behavior.