Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension

We construct families of fundamental, dipole, and tripole solitons in the fractional Schrödinger equation (FSE) incorporating self-focusing cubic and defocusing quintic terms modulated by factors cos²x and sin²x, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the Lévy index (LI) that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles.