Fractional solitons with cubic dispersion

We report solitons in the presence of a cubic nonlinearity and piecewise cubic dispersion. This dispersion ensures that the associated group velocity of the light increases monotonically with frequency as required for the formation of optical solitons. The dispersion relation has a discontinuity in its third derivative, which in time corresponds to a nonlocal, fractional Laplacian operator. Our experiments show that the resulting solitons have a novel pulse length–energy relationship that is intermediate between conventional solitons of the nonlinear Schrödinger equation and pure-quartic solitons but differ from these solitons in other respects.