Pure quartic traveling wave solutions: a numerical study

We study a family of periodic traveling wave solution of a pure quartic generalized nonlinear Schrödinger equation (NLSE). We focus on dn-oidal-like solutions with a nonzero average component. After numerically finding a one-parameter family of solutions and comparing it to their conventional NLSE counterpart, we numerically solve the corresponding modulational instability problem. This shows a nontrivial trend, where the instability occurs in specific intervals of the parameter separated by stability islands. Numerical simulations confirm the soundness of this result, thus proving that high-order dispersion terms in an optical waveguide allow to observe the propagation of regular and stable comb-like spectra.