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Contrary to the common understanding, the Sine-Gordon equation in (1+2)dimensions does have N-soliton solutions for any N. The Hirota algorithm allowsfor the construction of static N-soliton solutions (i.e., solutions that do notdepend on time) of that equation for any N. Lorentz transforming the staticsolutions yields N-soliton solutions in any moving frame. They are scalarfunctions under Lorentz transformations. In an N-soliton solution in a movingframe, (N-2) of the (1+2)-dimensional momentum vectors of the solitons arelinear combinations of the two remaining vectors.

Static solitons, Lorentz invariance, and a new perspective on the integrability of the Sine Gordon equation in (1+2) dimensions