Periodic nonlinear Schrödinger equation with application to photonic crystals

被引：0
|
作者：
Pankov A. [1 ]
机构：
[1] Mathematics Department, College of William and Mary, Williamsburg
来源：
Milan Journal of Mathematics | 2005年 / 73卷 / 1期
关键词：
Critical point; Gap soliton; Nonlinear Schrödinger equation;
D O I：
10.1007/s00032-005-0047-8
中图分类号：
学科分类号：
摘要：
We present some results on existence of nontrivial solutions of periodic stationary nonlinear Schrödinger equations. We also sketch an application to nonlinear optics and discuss some open problems. © 2005 Birkhäuser Verlag, Basel/Switzerland.
引用
收藏
页码：259 / 287
页数：28
相关论文
共 50 条
  • [21] Stability of periodic waves for the defocusing fractional cubic nonlinear Schrõdinger equation
    Borluk, Handan
    Muslu, Gulcin M.
    Natali, Fabio
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2024, 133
  • [22] The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions
    B. Deconinck
    A. S. Fokas
    J. Lenells
    Letters in Mathematical Physics, 2021, 111
  • [23] Quasi-periodic solutions with prescribed frequency in a nonlinear Schrödinger equation
    Xiu-Fang Ren
    Science China Mathematics, 2010, 53 : 3067 - 3084
  • [24] Robustness and stability of doubly periodic patterns of the focusing nonlinear Schrödinger equation
    Yin, H. M.
    Li, J. H.
    Zheng, Z.
    Chiang, K. S.
    Chow, K. W.
    CHAOS, 2024, 34 (01)
  • [25] Periodic solutions of a fractional Schrödinger equation
    Wang, Jian
    Du, Zhuoran
    APPLICABLE ANALYSIS, 2024, 103 (08) : 1540 - 1551
  • [26] On the spectral problem associated with the time-periodic nonlinear Schrödinger equation
    Jonatan Lenells
    Ronald Quirchmayr
    Mathematische Annalen, 2020, 377 : 1193 - 1264
  • [27] Quasi-periodic solutions with prescribed frequency in a nonlinear Schrdinger equation
    REN Xiu-Fang Department of Mathematics
    Science China(Mathematics), 2010, 53 (12) : 3067 - 3084
  • [28] On an inequality of Trudinger type and its application to a nonlinear Schrödinger equation
    Sh. M. Nasibov
    Mathematical Notes, 2006, 80 : 740 - 743
  • [29] A NONLINEAR SCHR?DINGER EQUATION WITH COULOMB POTENTIAL
    苗长兴
    张军勇
    郑继强
    Acta Mathematica Scientia, 2022, 42 (06) : 2230 - 2256
  • [30] A nonlinear Schrödinger equation with Coulomb potential
    Changxing Miao
    Junyong Zhang
    Jiqiang Zheng
    Acta Mathematica Scientia, 2022, 42 : 2230 - 2256
12345