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Patterns on liquid surfaces: Cnoidal waves, compactons and scaling. (English) Zbl 0952.76008
From the summary: We investigate localized patterns and nonlinear oscillation formations on the bounded free surface of ideal incompressible liquid. 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. We introduce a tentative expansion formula for the representation of the general solution of a nonlinear equation, for given initial conditions.
MSC:
76B25Solitary waves (inviscid fluids)
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction