We review the Levi-Civita theory, which reduces the study of the irrotational flow in a one-dimensional channel or the solution of a non-linear differential-functional partial differential equation for the velocity potential. We show how, by considering small perturbations in a shallow water channel, we can reduce the non-linear differential-functional equation to a complex Korteweg-de Vries equation which, for almost horizontal flow and for initial conditions independent of the vertical variable, reduces to the usual one.

Levi, D. (1994). LEVI-CIVITA THEORY FOR IRROTATIONAL WATER-WAVES IN A ONE-DIMENSIONAL CHANNEL AND THE COMPLEX KORTEWEG-DE VRIES EQUATION. THEORETICAL AND MATHEMATICAL PHYSICS, 99(3), 705-709 [10.1007/BF01017056].

LEVI-CIVITA THEORY FOR IRROTATIONAL WATER-WAVES IN A ONE-DIMENSIONAL CHANNEL AND THE COMPLEX KORTEWEG-DE VRIES EQUATION

LEVI, Decio
1994-01-01

Abstract

We review the Levi-Civita theory, which reduces the study of the irrotational flow in a one-dimensional channel or the solution of a non-linear differential-functional partial differential equation for the velocity potential. We show how, by considering small perturbations in a shallow water channel, we can reduce the non-linear differential-functional equation to a complex Korteweg-de Vries equation which, for almost horizontal flow and for initial conditions independent of the vertical variable, reduces to the usual one.
Levi, D. (1994). LEVI-CIVITA THEORY FOR IRROTATIONAL WATER-WAVES IN A ONE-DIMENSIONAL CHANNEL AND THE COMPLEX KORTEWEG-DE VRIES EQUATION. THEORETICAL AND MATHEMATICAL PHYSICS, 99(3), 705-709 [10.1007/BF01017056].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/124599
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