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非线性Schrdinger方程(Ⅰ):Bose-Einstein凝聚和怪波现象 被引量：7

Nonlinear Schrdinger Equation(Ⅰ):Bose-Einstein Condensation and Rogue Waves
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摘要 非线性Schr(o|¨)dinger方程是非线性科学领域的最基本的方程之一,本文综述该方程的两个有趣的现象:怪波和Bose-Einstein凝聚,最后提出一些相关的公开问题. Nonlinear Schrodinger equation（NLS） is one of the most fundamental equation in the theory of nonlinear sciences. In this paper, we survey some recent progress on the rogue wave and Bose-Einstein condensation phenomena of NLS, and some open problems related to NLS are presented.
作者 郭柏灵
机构地区 北京应用物理与计算数学研究所
出处 《数学进展》 CSCD 北大核心 2011年第4期393-399,共7页 Advances in Mathematics（China）
关键词 非线性SCHRODINGER方程 Bose—Einstein凝聚 怪波 孤立子 nonlinear Sehrodinger equation Bose-Einstein condensation rogue wave soliton
分类号 O175.29 [理学—基础数学]
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参考文献8

  • 1Ankiewicz, A., Clarkson, P.A., Akhmediev, N., Rogue waves, rational solutions, the Patterns of their zeros and integral ralations, J. Phys. A: Math. Theor., 2010, 43: 122002.
  • 2Akhmediev, N., Ankiewicz, A., Soto-Crespo, J.M., Rogue waves and rational solutions of the nonlinear Schrodinger equation, Phys. Rev. E., 2009, 80: 026601.
  • 3Lin F., Lin T.C., Vortices in two dimensional Bose-Einstein Condensates. Geometry and nonlinear par- tial differential equations, Hangzhou, 2001, 87, 114, AMS/IP Stud. Adv. Math. 29, Amer. Math. Soc. Providence, RI, 2002.
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同被引文献28

  • 1Ablowitz M J, Clarkson P A. 1991. Solitons, Nonlinear Evolution E-quation and Inverse Scattering[ M] . Cambridge : Cambridge University Press.
  • 2Ablowitz M J, Prinari B, Trubatch A D. 2004. Discrete and Continuous Nonlinear Schrodinger Systems [ M]. Cambridge : Cambridge University Press.
  • 3Akhmediev N, Ankiewicz A. 2011. Modulation instability, Fermi-Pas-ta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation [ J]. Physical Review E,83 (4): 046603-10.
  • 4Ankiewicz A, Akhmediev N, Soto-Crespo J M. 2010. Discrete roguewaves of the Ablowitz-Ladik and Hirota equations[ J]. Physical Review E, 82(8) : 026602-7.
  • 5Geng X G,Dai H H,Zhang J Y. 2007. Decomposition of the discrete Ablowitz-Ladik hierarchy [ J ]. Studies in Applied Mathematics, 118 (3) : 281-312.
  • 6Guo B L, Ling L M. 2011. Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schrodinger Equations[ J]. Chinese Physics Letters, 28(11) : 110202-4.
  • 7Hirota R. 1971. Exact solution of the KdV equation for multiple collisions of solitons[ J]. Physical Review Letters, 27( 18) : 1192- 4.
  • 8Zhang D J,Chen S T. 2010. Symmetries for the Ablowitz - Ladik Hierarchy :Part I. Four-Potential Case [ J ]. Studies in Applied Mathematics, 125(4) : 393-418.
  • 9Zhang D J, Chen S T. 2010. Symmetries for the Ablowitz - Ladik Hierarchy :Part II. Integrable Discrete Nonlinear Schrodinger Equations and Discrete AKNS Hierarchy[ J]. Studies in Applied Mathematics, 125(4) : 419-443.
  • 10梁宗旗.具有波动算子的非线性Schrdinger方程的有限差分法[J].黑龙江大学自然科学学报,1998,15(1):1-4. 被引量：9

引证文献7

二级引证文献10

数学进展
2011年 第4期

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