Some properties of the complexification of the KdV equation

T. V. Red'kina


Abstract: An integrable complexification of the hierarchy of the KdV equation is constructed. A countable set of first integrals is found, along with the evolution of the scattering data for the complexification of the KdV equation obtained in [1]. Hirota's method is used to obtain some exact solutions of this equation. A representation of the complexification of the KdV equation as an equation of zero curvature is indicated.

UDC: 539.2

MSC: Primary 35Q53, 35Q58; Secondary 34A25, 35A25, 58F07

Received: 06.05.1991

 English version: Mathematics of the USSR-Izvestiya, 1992, 39:3, 1251–1261

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