Numerical simulation of singular solutions to the two‐dimensional cubic schrödinger equation
- 1 November 1984
- journal article
- research article
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 37 (6) , 755-778
- https://doi.org/10.1002/cpa.3160370603
Abstract
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 R2‐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.Keywords
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