Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise.

@article{Christiansen1996CollapseOS,
  title={Collapse of solitary excitations in the nonlinear Schr{\"o}dinger equation with nonlinear damping and white noise.},
  author={Morten H. Christiansen and Yuri Gaididei and Liselotte S. Johansson and Sune Olander Rasmussen and Yakimenko},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={1996},
  volume={54 1},
  pages={
          924-930
        }
}
We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schro ̈dinge equation~NLS!. Using a collective coordinate approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead result in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of… CONTINUE READING