Numerical simulations of the cubic nonlinear Schrödinger equation are presented in dimension N = 2. The emphasis is on a detailed mechanism of blow up. The numerical results indicate that the blow up is not restricted to the case where the problem is posed in the entire R 2 ‐space but also occurs with periodic boundary conditions. The structure of the solution as the singular time t * is approached has been investigated using examples with and without radial symmetry and/or periodicity. In most cases we observe that the amplitude develops something like the peaked self‐similar profile predicted by Zakharov and Synakh [38] which has a ( t * ‐ t ) ‐2/3 maximum amplitude and a ( t * ‐ t ) 2/3 width.
No takes yet. Share an insight, caveat, or question.
Sulem et al. (1984) studied this question.