HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

doi:10.1016/S0252-9602(15)30004-7

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 567-582.doi: 10.1016/S0252-9602(15)30004-7

HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

冯斌华¹, 赵敦², 孙春友²

1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China;
2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

收稿日期:2014-01-05 修回日期:2014-04-14 出版日期:2015-05-01 发布日期:2015-05-01
通讯作者: Binhua FENG E-mail:binhuaf@163.com
基金资助:
This work was supported by the NSFC Grants 10601021 and 11475073.

HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

Binhua FENG¹, Dun ZHAO², Chunyou SUN²

1. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China;
2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received:2014-01-05 Revised:2014-04-14 Online:2015-05-01 Published:2015-05-01
Contact: Binhua FENG E-mail:binhuaf@163.com
Supported by:
This work was supported by the NSFC Grants 10601021 and 11475073.

摘要/Abstract

摘要：

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 iψ_t+Δψ +φ(ωt)|ψ|^αψ+iζ(ωt)ψ= 0.Under some conditions, we show that as ω→∞, the solution ψ_ω will locally converge to the solution of the averaged equation iψ_t+Δψ +φ₀|ψ|^αψ+iζ₀ψ= 0 with the same initial condition in L^q((0, T),B_r^s,2)for all admissible pairs (q, r), where T ∈ (0,T_max). We also show that if the dissipation coefficient ζ₀ large enough, then,ψ_ω is global if ω is sufficiently large and ψ_ω converges to ψ in L^q((0,∞),B_r^s,2), for all admissible pairs (q, r). In particular, our results hold for both subcritical and critical nonlinearities.

关键词: Nonlinear Schrö, dinger equation, averaged equation, global existence, convergence

Abstract:

Key words: Nonlinear Schrö, dinger equation, averaged equation, global existence, convergence

中图分类号:

35B27

冯斌华, 赵敦, 孙春友. HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES[J]. 数学物理学报(英文版), 2015, 35(3): 567-582.

Binhua FENG, Dun ZHAO, Chunyou SUN. HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES[J]. Acta mathematica scientia,Series B, 2015, 35(3): 567-582.

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HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

HOMOGENIZATION FOR NONLINEAR SCHRÖDINGER EQUATIONS WITH PERIODIC NONLINEARITY AND DISSIPATION IN FRACTIONAL ORDER SPACES

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