Multi-hump solitons under fractional diffraction and inhomogeneous cubic nonlinearity in a quadratic potential

We demonstrate the existence and stability of various multi-hump soliton families within the nonlinear Schrödinger equation with inhomogeneous cubic nonlinearity and fractional diffraction, in the presence of a linear quadratic potential. The profiles, amplitudes, and powers of the three soliton families (the two-, three- and four-hump solitons) are investigated under different parameters, including the Lévy index, propagation constant, and the parameters of the nonuniform cubic nonlinearity. The amplitudes of the two- and three-hump solitons are little sensitive to the variations in the Lévy index, but are highly sensitive to the changes in the propagation constant. Furthermore, we report on two distinct types of four-hump solitons and their propagation under longitudinally modulated nonlinearity. Interestingly, a gradual increase or decrease in the parameter results in the stable regular propagation, while a sudden increase or decrease causes severe distortions and leads to unstable behavior of solitons.