Rate of blowup for solutions of the nonlinear Schrödinger equation at critical dimension
Abstract
A perturbation analysis with respect to the space dimension is used to construct singular solutions of the two-dimensional Schrödinger equation with cubic nonlinearity. These solutions blow up at a rate \{ln ln[(t*-t)-1]/(t*-t)\}1/2, in contrast to the behavior in three dimensions where there is no logarithmic correction. The form of such solutions is supported by the results of high-resolution numerical simulations.
- Publication:
-
Physical Review A
- Pub Date:
- October 1988
- DOI:
- 10.1103/PhysRevA.38.3837
- Bibcode:
- 1988PhRvA..38.3837L
- Keywords:
-
- Nonlinear Equations;
- Numerical Stability;
- Schroedinger Equation;
- Computerized Simulation;
- High Resolution;
- Refractivity;
- Space-Time Functions;
- Physics (General);
- 42.65.Bp;
- 42.65.Jx;
- Beam trapping self-focusing and defocusing;
- self-phase modulation