Suppressing the critical collapse of solitons by one-dimensional quintic nonlinear lattices

The stabilization of two-dimensional (2D) solitons in self-focusing Kerr media against the critical collapse with the help of nonlinear lattices (NLs), i.e., spatially periodic modulations of the local strength of the cubic nonlinearity, was recently investigated in detail. In one dimension (1D), the critical collapse is induced by the quintic self-focusing. Degenerate families of unstable localized modes which exist in these situations are usually called Townes solitons. We aim to explore a possibility of the stabilization of the 1D Townes solitons by means of NLs acting on the quintic or cubic–quintic (CQ) terms in the corresponding nonlinear-Schrödinger/Gross–Pitaevskii equation (NLSE/GPE). These settings may be realized in nonlinear optics and Bose–Einstein condensates (BECs). We develop the variational approximation (VA) for the CQ model, and use numerical methods to study the stability and mobility of solitons in both models, quintic and CQ. “Two-tier” and higher-order solitons, including dipole modes, are also found in the CQ medium (chiefly, in the case when the quintic nonlinearity tends to be self-defocusing). The stability region for fundamental solitons amounts to a narrow stripe in a parameter plane of the model with the quintic-only nonlinearity, being much broader in the case of the CQ nonlinearity.