Abstract
In a recent series of papers by Lou et al it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of -dimensional systems. We prove that the deformation algorithm introduced in (Lou et al 2023 J. High Energy Phys. 2023 018), applied to Lax integrable -dimensional systems, produces Lax integrable higher dimensional systems. The same property is enjoyed by the generalized deformation algorithm introduced in (Lou et al 2023 Chin. Phys. Lett. 40 020201); we present a novel example of a -dimensional deformation of KdV equation obtained by generalized deformation. The deformed systems obtained by such procedure, however, pose a serious challenge because most of the mathematical structures that the -dimensional systems possess are lost.
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