TY - JOUR
T1 - Nonlinear-damping continuation of the nonlinear Schrödinger equation - A numerical study
AU - Fibich, G.
AU - Klein, M.
N1 - Funding Information:
This research was partially supported by grant 1023/08 from the Israel Science Foundation (ISF) .
PY - 2012/3/1
Y1 - 2012/3/1
N2 - 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 iψt(t,x)+Δψ+| ψ|p-1ψ+iδ|ψ|q-1ψ=0, 0<δ≪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 δ 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.
AB - 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 iψt(t,x)+Δψ+| ψ|p-1ψ+iδ|ψ|q-1ψ=0, 0<δ≪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 δ 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.
KW - Continuation beyond the singularity
KW - NLS
KW - Nonlinear damping
UR - http://www.scopus.com/inward/record.url?scp=84855815621&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2011.11.008
DO - 10.1016/j.physd.2011.11.008
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AN - SCOPUS:84855815621
SN - 0167-2789
VL - 241
SP - 519
EP - 527
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 5
ER -