| 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 equatin 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 indepedent of the vertical variable, reduces to the usual one.Dipartimento di Fisica, Università di Roma III, Instituto Nazionale di Fisica Nucleare, Sezione di Roma, P.zale A. Moro 2, 00185 Roma, Italy. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 435–440, June, 1994. |
