Solutions with various structures for semilinear equations in ${\mathbb{R}}^n$ driven by fractional Laplacian

We study bounded solutions to the fractional equation $(-\Delta)^s u + u - |u|^{q-2}u = 0$in$\mathbb R^n$for$n\ge2$andsubcriticalexponent$q>2$. 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, quasi-periodic, breather type, etc.).