Self-Focusing with Fourth-Order Dispersion

We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion i ψₜ ± Δq ψ + |ψ|2 σ ψ = 0, in the isotropic mixed-dispersion NLS i ψₜ + Δ ψ +ε Δ² ψ + |ψ|2 σ ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.