Two-dimensional modulation instability and soliton clusters in nonlocal media with competing cubic-quintic nonlinearities

Using linear -stability analysis, two-dimensional modulation instability (MI) of plane wave is studied in nonlocal media with competing cubic-quintic (CQ) nonlinearities, which shows that MI can be effectively eliminated by strong nonlocality and competing quintic nonlinearity. Furthermore, propagation properties of higherorder soliton clusters, i.e., Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) solitons are also investigated. Bifurcated solutions of these solitons are obtained analytically with variational approach. We also demonstrate in detail the propagation dynamics of the HG and LG solitons with split -step Fourier transform.