We review the Levi-Civita theory that reduces the study of a stationary irrotational flow in a one-dimensional channel to the solution of a nonlinear differential functional equation for the velocity potential. We show how, for small flows and small perturbations about a reference velocity, we can reduce the nonlinear differential functional equation to a stationary complex Korteweg-de Vries equation. We study its one soliton solution and show that, due to its complex nature, there is a natural cutoff in its amplitude.

Levi, D., Sanielevici, M. (1996). Irrotational water waves and the complex Korteweg de Vries equation. PHYSICA D-NONLINEAR PHENOMENA, 98(2-4), 510-514 [10.1016/0167-2789(96)00109-1].

Irrotational water waves and the complex Korteweg de Vries equation

LEVI, Decio;
1996-01-01

Abstract

We review the Levi-Civita theory that reduces the study of a stationary irrotational flow in a one-dimensional channel to the solution of a nonlinear differential functional equation for the velocity potential. We show how, for small flows and small perturbations about a reference velocity, we can reduce the nonlinear differential functional equation to a stationary complex Korteweg-de Vries equation. We study its one soliton solution and show that, due to its complex nature, there is a natural cutoff in its amplitude.
1996
Levi, D., Sanielevici, M. (1996). Irrotational water waves and the complex Korteweg de Vries equation. PHYSICA D-NONLINEAR PHENOMENA, 98(2-4), 510-514 [10.1016/0167-2789(96)00109-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/119915
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