Royal Society Publishing

On the geometry of an integrable (2+1)–dimensional sine–Gordon system

W. K. Schief

Abstract

It is recorded that Darboux's method of linking the classical Lamé system governing triply orthogonal systems of surfaces with an integrable (2+1)–dimensional sine–Gordon equation may be extended and applied to the integrable two–component generalization of the latter introduced by Konopelchenko and Rogers. Thus, in a reinterpretation, this (2+1)–dimensional sine–Gordon system is shown to define particular (integrable) motions of surfaces.

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