Self-Focusing with Fourth-Order Dispersion

Source abstract

We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion $i \psi_t \pm \Delta^q \psi + |\psi|^{2 \sigma} \psi = 0,$ in the isotropic mixed-dispersion NLS $i \psi_t + \Delta \psi +\epsilon \Delta^2 \psi + |\psi|^{2 \sigma} \psi = 0$, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.