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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
