MA Rui,LI Chunhua.Asymptotic behavior of solutions to nonlinear Schrdinger systems with potentials in 2D[J].Journal of Yanbian University,2021,47(04):283-288.
一类具有位势的二维非线性薛定谔系统解的渐近行为
- Title:
- Asymptotic behavior of solutions to nonlinear Schrödinger systems with potentials in 2D
- 文章编号:
- 1004-4353(2021)04-0283-06
- Keywords:
- nonlinear Schrö; dinger equation; potentials; mass resonance; asymptotic behavior of solution
- 分类号:
- O175.29
- 文献标志码:
- A
- 摘要:
- 利用质量共振的性质、薛定谔方程的Strichartz估计、薛定谔算子的性质和先验估计的方法,讨论了一类具有位势的二维三次非线性薛定谔系统的小初值问题.证明了该问题整体解的存在性、解的时间衰减估计,并给出了解的长时间渐近行为.
- Abstract:
- The small initial value problem of a class of two - dimensional cubic nonlinear Schrödinger systems with potential is discussed by using the characters of mass resonance, the Strichartz estimates of Schrödinger equations, the properties of Schrödinger operators and the method of a priori estimates. The existence of the global solution and the time decay estimates of the solution are proved, and the long - time asymptotic behavior of the solution is given.
参考文献/References:
[1] GEORGIEV V, LI C H.On the scattering problem for the nonlinear Schrödinger equation with a potential in 2D[J].Physica D: Nonlinear Phenomena, 2019,398:208 - 218.
[2] KAWAHARA Y, SUNAGAWA H.Global small amplitude solutions for two - dimensional nonlinear Klein - Gordon systems in the presence of mass resonance[J].J Differential Equations, 2011,251(9):2549 - 2567.
[3] LI Z, ZHAO Z F.Decay and scattering of solutions to nonlinear Schrödinger equations with regular potentials for nonlinearities of sharp growth[J].J Math Study, 2017,50(3):277 - 290.
[4] CUCCAGNA S, GEORGIEV V, VISCIGLIA N.Decay and scattering of small solutions of pure power NLS in R with p>3 and with a potential[J].Communications on Pure and Applied Mathematics, 2014,67(2):957 - 981.
[5] HAYASHI N, OZAWA T.Scattering theory in weighted L2(Rn)spaces for some Schrödinger equations[J].Ann Inst H Poincaré Phys Théor, 1988,48(1):17 - 37.
[6] HAYASHI N, LI C H, NAUMKIN P I.On a system of nonlinear Schrödinger equations in 2D[J].Differential Integral Equations, 2011,24(5/6):417 - 434.
[7] KATAYAMA S, LI C H, SUNAGAWA H.A remark on decay rates of solutions for a system of quadratic nonlinear Schrödinger equations in 2D[J].Differential Integral Equations, 2014,27(3/4):301 - 312.
[8] LI C H.On a system of quadratic nonlinear Schrödinger equations and scale invariant spaces in 2D[J].Differential and Integral Equations, 2015,28(3/4):201 - 220.
相似文献/References:
[1]韩琦悦,李春花*.一类非线性薛定谔方程解的衰减估计[J].延边大学学报(自然科学版),2020,46(01):24.
HAN Qiyue,LI Chunhua*.Decay estimates of solutions to a class of nonlinear Schr?dinger equations[J].Journal of Yanbian University,2020,46(04):24.
[2]郭佳鑫,李春花.二维耗散非线性薛定谔方程解的时间衰减估计[J].延边大学学报(自然科学版),2023,(04):283.
GUO Jiaxin,LI Chunhua.Time decay estimates of solutions to dissipative nonlinear Schr?dinger equations in two space dimensions[J].Journal of Yanbian University,2023,(04):283.
备注/Memo
收稿日期: 2021-10-08
基金项目: 国家自然科学基金(11461074); 吉林省中青年科技创新领军人才及团队项目(20200301053RQ)
第一作者: 马瑞(1966—),女,在读硕士,研究方向为微分方程及其应用.
通信作者: 李春花(1977—),女(朝鲜族),博士,副教授,研究方向为微分方程及其应用.