Symmetry group and non-propagating solitons in the (2Â +Â 1)-dimensional sine-Gordon equation

Starting from the compact version of the (2 + 1)-dimensional sine-Gordon equation, the symmetry group and then the Lie symmetries and the related algebra can be obtained via a simple combination of a gauge transformation of the spectral function and the transformations of the space time variables. Thereout, applying the group transformation theorem on a two-straight-line soliton solution, one can derive two types of meaningful non-propagating dromion lattice excitations.