Continuations of the nonlinear Schrödinger equation beyond the singularity
Continuations of the nonlinear Schrödinger equation beyond the singularity
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 ring-type solutions, (3) a vanishing nonlinear-damping continuation and (4) a complex Ginzburg–Landau (CGL) continuation. Using asymptotic analysis, we explicitly calculate the limiting solutions beyond the singularity. …