1D solitons in cubic-quintic fractional nonlinear Schrödinger model

AbstractWe examine the properties of a soliton solution of the fractional Schrö dinger equation with cubic-quintic nonlinearity. Using analytical (variational) and numerical arguments, we have shown that the substitution of the ordinary Laplacian in the Schrödinger equation by its fractional counterpart with Lévy index $$\alpha$$ α permits to stabilize the soliton texture in the wide range of its parameters (nonlinearity coefficients and $$\alpha$$ α ) values. Our studies of $$\omega (N)$$ ω ( N ) dependence ($$\omega$$ ω is soliton frequency and N its norm) permit to acquire the regions of existence and stability of the fractional soliton solution. For that we use famous Vakhitov-Kolokolov…