留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

非线性扰动耦合Schrödinger系统激波的近似解法

姚静荪 欧阳成 陈丽华 莫嘉琪

姚静荪, 欧阳成, 陈丽华, 莫嘉琪. 非线性扰动耦合Schrödinger系统激波的近似解法[J]. 应用数学和力学, 2012, 33(12): 1477-1486. doi: 10.3879/j.issn.1000-0887.2012.12.009
引用本文: 姚静荪, 欧阳成, 陈丽华, 莫嘉琪. 非线性扰动耦合Schrödinger系统激波的近似解法[J]. 应用数学和力学, 2012, 33(12): 1477-1486. doi: 10.3879/j.issn.1000-0887.2012.12.009
YAO Jing-sun, OUYANG Cheng, CHEN Li-hua, MO Jia-qi. Approximate Solving Method of Shock for Nonlinear Disturbed Coupled Schrödinger System[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1477-1486. doi: 10.3879/j.issn.1000-0887.2012.12.009
Citation: YAO Jing-sun, OUYANG Cheng, CHEN Li-hua, MO Jia-qi. Approximate Solving Method of Shock for Nonlinear Disturbed Coupled Schrödinger System[J]. Applied Mathematics and Mechanics, 2012, 33(12): 1477-1486. doi: 10.3879/j.issn.1000-0887.2012.12.009

非线性扰动耦合Schrödinger系统激波的近似解法

doi: 10.3879/j.issn.1000-0887.2012.12.009
基金项目: 国家自然科学基金资助项目(41175058);中国科学院战略性先导科技专项应对气候变化的碳收支认证及相关问题基金资助项目(XDA01020304);安徽高校省级自然科学研究基金资助项目(KJ2011A135);浙江省自然科学基金资助项目(Y6110502);江苏省自然科学基金资助项目(BK2011042);福建省教育厅基金项目(A类)课题资助项目(JA10288)
详细信息
    作者简介:

    姚静荪(1956—),女,安徽黟县人,教授(E-mail: jsyao@mail.ahnu.edu.cn);莫嘉琪(1937—),男,浙江德清人,教授(联系人.Tel:+86-553-3869642; E-mail: mojiaqi@mail.ahnu.edu.cn).

  • 中图分类号: O175.29

Approximate Solving Method of Shock for Nonlinear Disturbed Coupled Schrödinger System

  • 摘要: 研究了一类非线性扰动耦合Schrödinger系统.利用精确解与近似解相关联的特殊技巧,首先讨论了对应典型的耦合系统,利用投射法得到了精确的激波行波解.再利用近似方法得到了扰动耦合Schrödinger系统的行波渐近解.
  • [1] Parkes E J, Duffy B R, Abbott P C. Some periodic and solitary travellingwave solutions of the short-pulse equation[J]. Chaos Solitons Fractals, 2008, 38(1): 154-159.
    [2] Sirendaoreji J S. Auxiliary equation method for solving nonlinear partial differential equations[J]. Phys Lett A, 2003, 309(5/6): 387-396.
    [3] McPhaden M J, Zhang D. Slowdown of the meridional overturning circulation in the upper Pacific ocean[J]. Nature, 2002, 415(3): 603-608.
    [4] 潘留仙, 左伟明, 颜家壬. LandauGinzburgHiggs方程的微扰理论[J]. 物理学报, 2005, 54(1): 1-5.(PAN Liu-xian, ZUO Wei-ming, YAN Jia-ren. The theory of the perturbation for Landau-Ginzburg-Higgs equation[J]. Acta Phys Sin, 2005, 54(1): 1-5.(in Chinese)) 
    [5] 封国林, 戴兴刚, 王爱慧, 丑纪范. 混沌系统中可预报性的研究[J]. 物理学报, 2001, 50(4): 606-611.(FENG Guo-lin, DAI Xing-gang, WANG Ai-hui, CHOU Ji-fan. On numerical predictability in the chaos system[J]. Acta Phys Sin, 2001, 50 (4): 606-611.(in Chinese)) 
    [6] Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method[M]. New York: CRC Press Co, 2004. 
    [7] He J H, Wu X H. Construction of solitary solution and compactonlike solution by variational iteration method[J]. Chaos, Solitions & Fractals, 2006, 29(1): 108-113. 
    [8] Ni W M, Wei J C. On positive solution concentrating on spheres for the GiererMeinhardt system[J]. J Differ Equations, 2006, 221(1): 158-189.
    [9] Bartier J P. Global behavior of solutions of a reactiondiffusion equation with gradient absorption in unbounded domains[J]. Asymptotic Anal, 2006, 46(3/4): 325-347. 
    [10] Libre J, da Silva P R, Teixeira M A. Regularization of discontinuous vector fields on R3 via singular perturbation[J]. J Dyn Differ Equations, 2007, 19(2): 309-331.
    [11] Guarguaglini F R, Natalini R. Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena[J]. Commun Partial Differ Equations, 2007, 32(2): 163-189.
    [12] MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J]. Science in China, Ser A, 1989, 32(11): 1306-1315. 
    [13] MO Jia-qi. Homotopic mapping solving method for gain fluency of laser pulse amplifier[J]. Science in China, Ser G, 2009, 39(5): 568-661. 
    [14] 莫嘉琪, 林一骅, 林万涛. 海-气振子厄尔尼诺-南方涛动模型的近似解[J]. 物理学报, 2010, 59(10):67076711.(MO Jia-qi, LIN Yi-hua, LIN Wan-tao. Approximate solution of seaair oscillator for El Ninosouthern oscillation model[J]. Acta Phys Sin, 2010, 59(10):6707-6711.(in Chinese)) 
    [15] MO Jia-qi, LIN Su-rong. The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation[J]. Chin Phys B, 2009, 18(9): 3628-3631.
    [16] MO Jia-qi.Solution of travelling wave for nonlinear disturbed long-wave system[J]. Commun Theor Phys, 2011, 55(3): 387-390.
    [17] MO Jia-qi, CHEN Xian-feng. Homotopic mapping method of solitary wave solutions for generalized complex Burgers equation[J]. Chin Phys B, 2010, 19(10): 100203.
    [18] 李帮庆, 马玉兰, 徐美萍, 李阳. 耦合Schrödinger系统的周期振荡折叠孤子[J]. 物理学报, 2011, 60(6): 060203.(LI Bang-qing, MA Yu-lan, XU mei-ping, LI Yang. Folded soliton with periodic vibration for a nonlinear coupled Schrödinger system[J]. Acta Phys Sin, 2011, 60(6): 060203.(in Chinese)) 
    [19] Barbu L, Morosanu G. Singularly Perturbed Boundary Value Problems[M]. Basel: Birkhauserm Verlag A G, 2007.
    [20] de Jager E M, JIANG Furu. The Theory of Singular Perturbation[M]. Amsterdam: North Holland Publishing, 1996.
  • 加载中
计量
  • 文章访问数:  1894
  • HTML全文浏览量:  70
  • PDF下载量:  1151
  • 被引次数: 0
出版历程
  • 收稿日期:  2011-10-13
  • 修回日期:  2012-04-23
  • 刊出日期:  2012-12-15

目录

    /

    返回文章
    返回