Spin waves in a two-sublattice antiferromagnet. A self-similar solution of the Landau-Lifshitz equation

•Spin waves in a uniaxial two-sublattice antiferromagnet are investigated.•A self-similar solution of the Landau-Lifshitz equation is found.•The self-similar solution we found admits nonlinear spin waves.•The space transformations are mathematically analogous to relativistic transformations.

In the paper, spin waves in a uniaxial two-sublattice antiferromagnet are investigated. A new class of self-similar solutions of the Landau-Lifshitz equation is obtained and, therefore, a new type of spin waves is described. Examples of solutions of the found class are presented. New type of solution admits both linear and non-linear spin waves, including solitons. Space transformations used in the solution are mathematically analogous to the relativistic transformations.