On the spectral transform of a Korteweg-de Vries equation in two spatial dimensions. (English) Zbl 0617.35119

Boiti, M.; Leon, J. J.-P.; Manna, M.; Pempinelli, F.

Inverse Probl. 2, 271-279 (1986).

From the authors’ abstract: An integro-differential generalisation of the Korteweg-de Vries equation is related to the spectral problem \((\partial^ 2_ x-\partial^ 2_ y-p(x,y))\phi (x,y;k)=0\). The Cauchy problem, associated with initial data decaying sufficiently rapidly at infinity, is linearised by an extension of the spectral transform technique to two spatial dimensions. The spectral data are explicitly defined in terms of the initial data and the inverse problem is formulated as a non-local Riemann-Hilbert boundary-value problem.

Reviewer: E.Malec

MSC:

35Q99	Partial differential equations of mathematical physics and other areas of application
35Q15	Riemann-Hilbert problems in context of PDEs
45K05	Integro-partial differential equations

Keywords:

integro-differential generalisation; Korteweg-de Vries equation; Cauchy problem; spectral transform; spectral data; non-local Riemann-Hilbert boundary-value problem