Application of the inverse spectral transform (IST) to the Korteweg-deVries and other non-linear partial differential equations in 2 dimensions (one space and one time) has been worked out in detail.

But 3 dimensional examples (two spatial dimensions) are much more scarce. The known examples (e.g. Kadomtsev–Petviashvili (KP) equation) have been described as "one and a half" dimensional problems, since the "soliton" solutions only involve two plane solitons interacting obliquely.