Modulation instability, solitons, and interactions in one-dimensional competing cubic-quintic nonlinear media with fourth-order diffraction

Modulation instability of one-dimensional plane waves, fundamental solitons, and interactions are investigated in competing cubic-quintic nonlinear media with fourth-order diffraction (FOD). Analytical results of the growth rate of modulation instability spectra are obtained with linear-stability analysis and confirmed numerically. Plane waves can propagate stably when modulation instability can be suppressed by FOD and competing nonlinearities. In addition, bifurcated solutions of fundamental Gaussian-type solitons are obtained by using a variational approach. Numerical simulations show that solitons are unstable (stable) in the regime of normal (anomalous) FOD. Interactions of in-phase and out-of-phase solitons are also demonstrated numerically, which show that normal (anomalous) FOD weakens (strengthens) the attractions of in-phase solitons and also weakens (strengthens) the repulsions of out-of phase solitons. It is also demonstrated that competing self-defocusing quintic nonlinearities always strengthen the attractive (repulsive) force between in-phase (out-of-phase) solitons.