Patterns on liquid surfaces: cnoidal waves, compactons and scaling
摘要
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.
引用
@article{arxiv.physics/0003077,
title = {Patterns on liquid surfaces: cnoidal waves, compactons and scaling},
author = {Andrei Ludu and Jerry P. Draayer},
journal= {arXiv preprint arXiv:physics/0003077},
year = {2009}
}
备注
14 pages RevTex, 5 figures in ps