The possibilities of formation and detection of the electromagnetic soliton-like wave in superlattices based on semi-Dirac crystals have been considered. The field of soliton-like wave obeys the d'Alembert equation which takes into account the current induced in superlattice by this wave. Resulting equation has the form of nonlinear Klein-Gordon equation. Some approximate methods of finding of kink solutions of obtained equation have been reviewed. The dependence of kinks parameters on the structure parameters of material has been analyzed. The new periodical solutions of considered equation have been found. The dependence of period of nonlinear electromagnetic wave which propagates in superlattice on the nonlinearity parameter has been studied. The phenomena of spontaneous doubling of frequency and spontaneous rectification of nonlinear wave in superlattice have been predicted.
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