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

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


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
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