This article is cited in 10 papers

Levi–Civita theory for irrotational water waves in a one dimensional channel and the complex Korteweg–de Vries equation

D. Levi

INFN — National Institute of Nuclear Physics

Abstract: We review Levi–Civita theory that 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 that, for almost horizontal flow and for initial conditions independent from the vertical variable, reduces to the usual one.

 English version: Theoretical and Mathematical Physics, 1994, 99:3, 705–709

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