New classes of solutions to semilinear equations in $\mathbb R^n$ with fractional Laplacian

We study bounded solutions to the fractional equation
$$ (-\Delta)^s u + u - |u|^{q-2}u = 0 $$
in $\mathbb R^n$ for $n\ge2$ and subcritical exponent $q>2$. Applying the variational approach based on concentration arguments and symmetry considerations which was introduced by Lerman, Naryshkin and Nazarov (2020) we construct several types of solutions with various structures (radial, rectangular, triangular, hexagonal, breather type, etc.), both positive and sign-changing.