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

强非线性波动方程孤子行波解

冯依虎1 2

冯依虎1, 2. 强非线性波动方程孤子行波解[J]. 应用数学和力学, 2019, 40(1): 89-96. doi: 10.21656/1000-0887.390054
引用本文: 冯依虎1, 2. 强非线性波动方程孤子行波解[J]. 应用数学和力学, 2019, 40(1): 89-96. doi: 10.21656/1000-0887.390054
FENG Yihu1, 2. Solitary Travelling Wave Solutions to Strongly Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2019, 40(1): 89-96. doi: 10.21656/1000-0887.390054
Citation: FENG Yihu1, 2. Solitary Travelling Wave Solutions to Strongly Nonlinear Wave Equations[J]. Applied Mathematics and Mechanics, 2019, 40(1): 89-96. doi: 10.21656/1000-0887.390054

强非线性波动方程孤子行波解

doi: 10.21656/1000-0887.390054
基金项目: 国家自然科学基金(41275062);安徽省教育厅自然科学基金(重点项目)(KJ2017A702);安徽省高校优秀青年人才支持计划(重点项目)(gxyqZD2016520)
详细信息
    作者简介:

    冯依虎(1982—),男,副教授,硕士(E-mail: fengyihubzxy@163.com).

  • 中图分类号: O175.26

Solitary Travelling Wave Solutions to Strongly Nonlinear Wave Equations

Funds: The National Natural Science Foundation of China(41275062)
  • 摘要: 研究了一个强非线性波动方程.利用泛函分析变分迭代方法,首先构造了一个变分, 求出相应的Lagrange乘子;其次构造一个解的变分迭代, 选取初始孤子波;最后利用迭代方法依次求出各次孤子波的近似解.该方法是一个简单可行的近似求解非线性方程的方法
  • [1] MCPHADEN M J, ZHANG D. Slowdown of the meridional overturning circulation in the upper Pacific Ocean[J]. Nature,2002,415(6872): 603-608.
    [2] LOUTSENKO I. The variable coefficient Hele-Shaw problem, integrability and quadrature identities[J]. Communications in Mathematical Physics,2006,268(2): 465-479.
    [3] GEDALIN M. Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description[J]. Physics of Plasmas,1998,5(1): 127-132.
    [4] PARKES E J. Some periodic and solitary travelling-wave solutions of the short-pulse equation[J]. Chaos Solitons & Fractals,2008,38(1): 154-159.
    [5] GU Daifang, PHILANDER S G H. Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics[J]. Science,1997,275(5301): 805-807.
    [6] 马松华, 强继业, 方建平. (2+1)维Boiti-Leon-Pempinelli系统的混沌行为及孤子间的相互作用[J]. 物理学报, 2007,56(2): 620-626.(MA Songhua, QIANG Jiye, FANG Jianping. The interaction between solitons and chaotic behaviours of (2+1)-dimensional Boiti-Leon-Pempinelli system[J]. Acta Physica Sinica,2007,56(2): 620-626.(in Chinese))
    [7] 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 Liuxian, ZUO Weiming, YAN Jiaren. The theory of the perturbation for Landau-Ginzburg-Higgs equation[J]. Acta Physica Sinica,2005,54(1): 1-5.(in Chinese))
    [8] 吴国将, 韩家骅, 史良马, 等. 一般变换下双Jacobi椭圆函数展开法及应用[J]. 物理学报, 2006,55(8): 3858-3863.(WU Guojiang, HAN Jiahua, SHI Liangma, et al. Double Jacobian elliptic function expansion method under a general function transform and its applications[J]. Acta Physica Sinica,2006,55(8): 3858-3863.(in Chinese))
    [9] 马松华, 吴小红, 方建平, 等. (3+1)维Burgers系统的新精确解及其特殊孤立子结构[J]. 物理学报, 2008,57(1): 11-17.(MA Songhua, WU Xiaohong, FANG Jianping, et al. New exact solutions and special soliton structures for the (3+1)-dimensional Burgers system[J]. Acta Physica Sinica,2008,57(1): 11-17.(in Chinese))
    [10] 李帮庆, 马玉兰. (G′/G)展开法和(2+1)维非对称Nizhnik-Novikov-Veselov系统的新精确解[J]. 物理学报,2009,58(7): 4373-4378.(LI Bangqing, MA Yulan.(G′/G)-expansion method and new exact solutions for (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov system[J]. Acta Physica Sinica,2009,58(7): 4373-4378.(in Chinese))
    [11] 周振春, 马松华, 方建平, 等. (2+1)维孤子系统的多孤子解和分形结构[J]. 物理学报, 2010,59(11): 7540-7545.(ZHOU Zhenchun, MA Songhua, FANG Jianping, et al. Multi-soliton solutions and fractal structures in a (2+1)-dimensional soliton system[J]. Acta Physica Sinica,2010,59(11): 7540-7545.(in Chinese))
    [12] 高亮, 徐伟, 唐亚宁, 等. 一类广义Boussinesq方程和Boussinesq-Burgers方程新的显式精确解[J]. 物理学报, 2007,56(4): 1860-1869.(GAO Liang, XU Wei, TANG Yaning, et al. New explicit exact solutions of one type of generalized Boussinesq equations and the Boussinesq-Burgers equation[J]. Acta Physica Sinica,2007,56(4): 1860-1869.(in Chinese))
    [13] 李向正, 李修勇, 赵丽英, 等. Gerdjikov-Ivanov方程的精确解[J]. 物理学报, 2008,57(4): 2031-2034.(LING Xiangzheng, LI Xiuyong, ZHANG Liying, et al. Exact solutions of Gerdjikov-Ivanov equation[J]. Acta Physica Sinica,2008,57(4): 2031-2034.(in Chinese))
    [14] 石兰芳, 聂子文. 应用全新G′/(G+G′)展开方法求解广义非线性Schrdinger方程和耦合非线性Schrdinger方程组[J]. 应用数学和力学, 2017, 38(5): 539-552.(SHI Lanfang, NIE Ziwen. Solutions to the nonlinear Schrdinger equation and coupled nonlinear Schrdinger equations with a new G′/(G+G′)-expansion method[J]. Applied Mathematics and Mechanics,2017, 38(5): 539-552. (in Chinese))
    [15] 石兰芳, 莫嘉琪. 一类强非线性方程Robin问题奇摄动解[J]. 应用数学, 2017, 30(2): 247-251.(SHI Lanfang, MO Jiaqi. A class of singular perturbation solutions to strong nonlinear equation Robin problems[J]. Mathematica Applicata,2017, 30(2): 247-251.(in Chinese))
    [16] FENG Yihu, MO Jiaqi. Asymptotic solution for singularly perturbed fractional order differential equation[J]. Journal of Mathematics,2016,36(2): 239-245.
    [17] FENG Yihu, CHEN Xianfeng, MO Jiaqi. The shock wave solution of a class of singularly perturbed problem for generalized nonlinear reaction diffusion equation[J]. Mathematica Applicata,2017,30(1): 1-7.
    [18] 冯依虎, 莫嘉琪. 一类非线性非局部扰动LGH方程的孤子行波解[J]. 应用数学和力学, 2016,37(4): 426-433.(FENG Yihu, MO Jiaqi. Soliton travelling wave solutions to a class of nonlinear nonlocal disturbed LGH equations[J]. Applied Mathematics and Mechanics,2016,37(4): 426-433.(in Chinese))
    [19] 冯依虎, 石兰芳, 莫嘉琪. 关于将飞秒脉冲激光用于纳米金属薄膜传导系统的研究[J]. 工程数学学报, 2017,34(1): 13-20.(FENG Yihu, SHI Lanfang, MO Jiaqi. Study of transfers system for femtosecond pulse laser to nano metal film[J]. Chinese Journal of Engineering Mathematics,2017,34(1): 13-20.(in Chinese))
    [20] 冯依虎, 陈怀军, 莫嘉琪. 一类非线性奇异摄动自治微分系统的渐近解[J]. 应用数学和力学, 2017,38(5): 355-363.(FENG Yihu, CHEN Huaijun, MO Jiaqi. Asymptotic solution to a class of nonlinear singular perturbation autonomic differential system[J]. Applied Mathematics and Mechanics,2017,38(5): 355-363.(in Chinese))
    [21] 冯依虎, 林万涛, 莫嘉琪. 大气中尘埃扩散方程行波解[J]. 吉林大学学报(理学版), 2016,54(2): 234-240.(FENG Yihu, LIN Wantao, MO Jiaqi. Travelling wave solution for dust diffusion equation in atmosphere[J]. Journal of Jilin University(Science Edition),2016,54(2): 234-240.(in Chinese))
    [22] 冯依虎, 林万涛, 莫嘉琪. 一类大气量子等离子流体动力学孤立子波渐近解[J]. 吉林大学学报(理学版), 2017,55(3): 474-480.(FENG Yihu, LIN Wantao, MO Jiaqi. Asymptotic solution for a class of quantum plasma fluid dynamics solitary wave in atmosphere[J]. Journal of Jilin University(Science Edition),2017,55(3): 474-480.(in Chinese))
    [23] 冯依虎, 莫嘉琪. 一类广义奇摄动非线性双曲型积分-微分方程模型[J]. 吉林大学学报(理学版), 2017,55(5): 1055-1060.(FENG Yihu, MO Jiaqi. A class of generalized nonlinear hyperbolic integral-differential equation with singular perturbation model[J]. Journal of Jilin University(Science Edition),2017,55(5): 1055-1060.(in Chinese))
    [24] LEBEDEV L P, CLOUD M J. The Calculus of Variations and Functional Analysis With Optimal Control and Applications in Mechanics [M]. New York: World Scientific, 2003.
    [25] 何吉欢. 工程和科学计算中的近似非线性分析方法[M]. 郑州: 河南科学技术出版社, 2002.(HE Jihuan. Approximate Nonlinear Analytical Methods in Engineering and Sciences [M]. Zhengzhou: Henan Science and Technology Press, 2002.(in Chinese))
    [26] DE JAGER M, JIANG F R. The Theory of Singular Perturbations [M]. Amsterdam: North-Holland Publishing Co, 1996.
    [27] BARBU L, MOROSANU G. Singularly Perturbed Boundary-Value Problems [M]. Basel: Birk-hauser, 2007.
  • 加载中
计量
  • 文章访问数:  1101
  • HTML全文浏览量:  166
  • PDF下载量:  689
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-02-03
  • 修回日期:  2018-04-17
  • 刊出日期:  2019-01-01

目录

    /

    返回文章
    返回