Localized patterns and nonlinear oscillation formations on the bounded free surface of an ideal incompressible liquid are investigated. Cnoidal modes, solitons and compactons, as traveling non-axially symmetric shapes are discussed. A finite-difference differential generalized Korteweg-de Vries (KdV) equation is shown to describe the three-dimensional motion of the fluid surface, and in the limit of long and shallow channels one recovers the well-known KdV equation. A tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial conditions is introduced. The model is useful in multilayer fluid dynamics, cluster formation, and nuclear physics since, up to an overall scale, these systems display a free liquid surface behavior. Copyright © 1998 Elsevier Science B.V.
Publication Source (Journal or Book title)
Physica D: Nonlinear Phenomena
Ludu, A., & Draayer, J. (1998). Patterns on liquid surfaces: Cnoidal waves, compactons and scaling. Physica D: Nonlinear Phenomena, 123 (1-4), 82-91. https://doi.org/10.1016/S0167-2789(98)00113-4