Optical collapse is a fascinating research topic. The propagation of intense laser beams in a
transparent medium is usually modeled by the two-dimensional nonlinear Schrödinger …

We prove global wellposedness and scattering for the Mass-critical homogeneous fourth-
order Schrödinger equation in high dimensions n≥ 5, for general L2 initial data in the …

We study the effect of a fourth-order derivative term in the diffusion of Brownian particles
confined to a narrow 2D channel whose longitudinal coordinate is larger than the …

We use asymptotic analysis and numerical simulations to study peak-type singular solutions
of the supercritical biharmonic nonlinear Schrödinger equation. These solutions have a …

We consider singular solutions of the L^2-critical biharmonic nonlinear Schrödinger
equation. We prove that the blowup rate is bounded by a quartic-root, the solution …

When mathematical and computational dynamic models reach infinity in finite time,
extending analysis and numerics beyond it becomes a notorious challenge. We suggest …

We present new singular solutions of the biharmonic nonlinear Schrödinger equation (NLS)
These solutions collapse with the quasi-self-similar ring profile, where L (t) is the ring width …

We present four continuations of the critical nonlinear Schrödinger equation (NLS) beyond
the singularity:(1) a sub-threshold power continuation,(2) a shrinking-hole continuation for …

We study the nonlinear-damping continuation of singular solutions of the critical and
supercritical NLS. Our simulations suggest that for generic initial conditions that lead to …

This paper is concerned with the Cauchy problem for the biharmonic nonlinear Schrödinger
equation with L2-super-critical nonlinearity. By establishing the profile decomposition of …