dorsal/arxiv
View SchemaPatterns on liquid surfaces: cnoidal waves, compactons and scaling
| Authors | Andrei Ludu, Jerry P. Draayer |
|---|---|
| Categories | |
| ArXiv ID | physics/0003077 |
| URL | https://arxiv.org/abs/physics/0003077 |
| DOI | 10.1016/S0167-2789(98)00113-4 |
| Journal | Physica D {\bf 123} (1998) 82 |
Abstract
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.
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"abstract": "Localized patterns and nonlinear oscillation formation on the bounded free\nsurface of an ideal incompressible liquid are analytically investigated .\nCnoidal modes, solitons and compactons, as traveling non-axially symmetric\nshapes are discused. A finite-difference differential generalized Korteweg-de\nVries equation is shown to describe the three-dimensional motion of the fluid\nsurface and the limit of long and shallow channels one reobtains the well known\nKdV equation. A tentative expansion formula for the representation of the\ngeneral solution of a nonlinear equation, for given initial condition is\nintroduced on a graphical-algebraic basis. The model is useful in multilayer\nfluid dynamics, cluster formation, and nuclear physics since, up to an overall\nscale, these systems display liquid free surface behavior.",
"arxiv_id": "physics/0003077",
"authors": [
"Andrei Ludu",
"Jerry P. Draayer"
],
"categories": [
"physics.flu-dyn",
"nlin.PS",
"physics.atm-clus"
],
"doi": "10.1016/S0167-2789(98)00113-4",
"journal_ref": "Physica D {\\bf 123} (1998) 82",
"title": "Patterns on liquid surfaces: cnoidal waves, compactons and scaling",
"url": "https://arxiv.org/abs/physics/0003077"
},
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