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 -