Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4663791 | Acta Mathematica Scientia | 2015 | 16 Pages |
Abstract
We study the nonlinear Schrödinger equation with time-oscillating nonlinearity and dissipation originated from the recent studies of Bose-Einstein condensates and optical systems which reads iψt+Δψ+φ(ωt)|ψα|ψ+iς(ωt)ψ=0. Under some conditions, we show that as ω→∞, the solution ψω will locally converge to the solution of the averaged equation iψt+Δψ+φ0|ψα|ψ+iζ0ψ=0 with the same initial condition in for all admissible pairs (q,r),where T∈(0,Tmax). We also show that if the dissipation coefficient ζo large enough, then, ψω is global if ω is sufficiently large and ψω converges to for all admissible pairs (q,r) In particular, our results hold for both subcritical and critical nonlinearities.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)