Nonlinear-damping continuation of the nonlinear Schrodinger equation - A numerical study

作者：Fibich G^*; Klein M

来源：Physica D: Nonlinear Phenomena , 2012, 241(5): 519-527.

DOI：10.1016/j.physd.2011.11.008

• NLS
• Continuation beyond the singularity
• Nonlinear damping

We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in the undamped NLS, the solution of the weakly-damped NLS
i psi(t)(t, x) + Delta psi + vertical bar psi vertical bar(p-1)psi + i delta vertical bar psi vertical bar(q-1)psi = 0, 0 < delta << 1.
is highly asymmetric with respect to the singularity time, and the post-collapse defocusing velocity of the singular core goes to infinity as the damping coefficient delta goes to zero. In the special case of the minimal-power blowup solutions of the critical NLS, the continuation is a minimal-power solution with a higher (but finite) defocusing velocity, whose magnitude increases monotonically with the nonlinear damping exponent q.

• 出版日期2012-3-1