非线性扰动广义NNV系统的孤立子渐近行波解

史娟荣; 吴钦宽; 莫嘉琪

doi:10.3879/j.issn.1000-0887.2015.09.011

非线性扰动广义NNV系统的孤立子渐近行波解

doi: 10.3879/j.issn.1000-0887.2015.09.011

¹安徽机电职业技术学院, 安徽芜湖 241002;²南京工程学院数理系, 南京 211167;³安徽师范大学数学系, 安徽芜湖 241003;⁴上海交通大学数学系,上海 200240

基金项目: 国家自然科学基金(11202106)

详细信息

作者简介:
史娟荣(1981—), 女，安徽宣城人, 副教授, 硕士（E-mail: ahjdshjr@126.com）;莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

中图分类号: O175.29
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出版历程
- 收稿日期: 2015-03-05
- 修回日期: 2015-06-15
- 刊出日期: 2015-09-15

Asymptotic Travelling Wave Soliton Solutions for Nonlinear Disturbed Generalized NNV Systems

¹Anhui Technical College of Mechanical and Electrical Engineering,Wuhu, Anhui 241002, P.R.China;²Department of Mathematics & Physics, Nanjing Institute of Technology, Nanjing 211167, P.R.China;³Department of Mathematics, Anhui Normal University,Wuhu, Anhui 241003, P.R.China;⁴Department of Mathematics, Shanghai Jiao Tong University,Shanghai 200240, P.R.China

Funds: The National Natural Science Foundation of China(11202106)

摘要

摘要: 采用了一个简单而有效的技巧，研究一类非线性扰动广义NNV(Nizhnik-Novikov-Veselov)系统.首先用待定系数法得到一个相应典型系统的孤立子解.其次构造一个广义泛函式，并对它进行变分计算,利用变分原理求出对应的Lagrange乘子,并由此构造一个特殊的变分迭代关系式.然后依次求出原非线性扰动广义NNV系统的孤立子渐近行波解.最后通过举例,说明了使用该方法得到的近似解具有简单而有效的优点.
- 孤立子 /
- 扰动NNV系统 /
- 迭代方法
Abstract: A class of nonlinear disturbed generalized NNV (NizhnikNovikovVeselov) system was addressed with a simple and valid technique. Firstly, the soliton solution to the corresponding typical differential system was obtained by means of the undetermined coefficient method. Secondly, a generalized functional equation was built and variationally calculated, and the corresponding Lagrange multiplier was derived according to the variation principle. Thereby, a special variational iteration relation expression was constructed. Then, the asymptotic travelling wave soliton solution for the original nonlinear disturbed generalized NNV system was attained successively. Finally, through an example, the proposed approximate analysis method is proved to be convenient and effective.
- soliton /
- disturbed Nizhnik-Novikov-Veselov system /
- iterative method

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参考文献(29)

[1]	McPhaden M J, Zhang D. Slowdown of the meridional overturning circulation in the upper Pacific Pcean[J].Nature,2002,415（6872）: 603-608.
[2]	GU Dai-fang, Philander S G H. Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics[J].Science,1997,275(7): 805-807.
[3]	马松华, 强继业, 方建平. (2+1)维Boiti-Leon-Pempinelli系统的混沌行为及孤立子间的相互作用[J]. 物理学报, 2007,56(2): 620-626.(MA Song-hua, QIANG Ji-ye, FANG Jian-ping. 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))
[4]	Loutsenko I. The variable coefficient Hele-Shaw problem, integrability and quadrature identities[J].Communications in Mathematical Physics,2006,268(2): 465-479.
[5]	Gedalin M. Low-frequency nonlinear stationary waves and fast shocks: hydrodynamical description[J].Physics of Plasmas,1998,5(1): 127-132.
[6]	Parkes E J. Some periodic and solitary travelling-wave solutions of the short-pulse equation[J].Chaos Solitons Fractals,2008,38(1): 154-159.
[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 Liu-xian, ZUO Wei-ming, YAN Jia-ren. The theory of the perturbation for Landau-Ginzburg-Higgs equation[J].Acta Physica Sinica,2005,54(1): 1-5.(in Chinese)）
[8]	封国林, 戴新刚, 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 Xin-gang, WANG Ai-hui , CHOU Ji-fan. On the numerical predictability in the chaos system[J].Acta Physica Sinica,2001,50(4): 606-611.(in Chinese)）
[9]	WENG Ming-liang. Solitary wave solutions for variant Boussinesq equations[J].Physics Letters A,1995, 199(3/4): 169-172.
[10]	吴国将, 韩家骅, 史良马, 张苗. 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 Guo-jiang, HAN Jia-hua, SHI Liang-ma, ZHANG Miao. 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))
[11]	李向正, 李修勇, 赵丽英, 张金良. Gerdjikov-Ivanov方程的精确解[J]. 物理学报, 2008,57(4): 2031-2034.(LI Xiang-zheng, LI Xiu-yong, ZHAO Li-ying, ZHANG Jin-liang. Exact solutions of Gerdjikov-Ivanov equation[J].Acta Physica Sinica,2008,57(4): 2031-2034.(in Chinese))
[12]	高亮, 徐伟, 唐亚宁, 申建伟. 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 Ya-ning, SHEN Jian-wei. 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]	马松华, 吴小红, 方建平, 郑春龙. (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 Song-hua, WU Xiao-hong, FANG Jian-ping, ZHENG Chun-long. 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))
[14]	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 Bang-qing, MA Yu-lan.(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))
[15]	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 Ji-huan.Approximate Analytical Methods in Engineering and Sciences [M]. Zhengzhou: Henan Science and Technology Press, 2002.(in Chinese))
[16]	Hovhannisyan G, Vulanovic R. Stability inequalities for one-dimensional singular perturbation problems[J].Nonlinear Studies,2008,15(4): 297-322.
[17]	Barbu L, Cosma E. Elliptic regularization for the nonlinear heat equation[J].Journal of Mathematical Analysis and Applications,2009,351(1): 392-399.
[18]	Ramos M. On singular perturbation of superlinear elliptic systems[J].Journal of Mathematical Analysis and Applications,2009,352(1): 246-258.
[19]	MO Jia-qi. Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China Ser A,1989,32(11): 1306-1315.
[20]	MO Jia-qi, LIN Wan-tao. Asymptotic solution for a class of sea-air oscillator model for El-Nino-southern oscillation[J].Chinese Physics B,2008,17(2): 370-372.
[21]	MO Jia-qi, LIN Wan-tao. Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J].Journal of Systems Science and Complexity,2008,20(1): 119-128.
[22]	MO Jia-qi, LIN Yi-hua, LIN Wan-tao, CHEN Li-hua. Perturbed solving method for interdecadal sea-air oscillator model[J].Chinese Geographical Science,2012,22(1): 42-47.
[23]	MO Jia-qi. A variational iteration solving method for a class of generalized Boussinesq equation[J].Chinese Physics Letters,2009,26(6): 060202.
[24]	FENG Yihu, MO Jiaqi. Asymptotic solution for singularly perturbed fractional order differential equation[J]. Journal of Mathematics,2016,36(2): 239-245.
[25]	MO Jia-qi. Homotopiv mapping solving method for gain fluency of a laser pulse amplifier[J].Science in China Ser G,2009,52(7): 1007-1010.
[26]	MO Jia-qi, LIN Wan-tao, WANG Hui. Variational iteration solution of a sea-air oscillator model for the ENSO[J].Progress in Natural Science,2007,17(2): 230-232.
[27]	史娟荣, 石兰芳, 莫嘉琪. 一类非线性强阻尼扰动发展方程的解[J]. 应用数学和力学, 2014,35(9): 1046-1054.(SHI Juan-rong, SHI Lan-fang, MO Jia-qi. The solutions for a class of nonlinear disturbed evolution equations[J].Applied Mathematics and Mechanics,2014,35(9): 1046-1054.(in Chinese))
[28]	吴钦宽. 一类非线性方程激波解的Sinc-Galerkin方法[J]. 物理学报, 2006,55(4): 1562-1564.(WU Qin-kuan. The shock solution for a class of the nonlinear equations by the Sinc-Galerkin method[J].Acta Physica Sinica,2006,55(4): 1562-1564.(in Chinese))
[29]	ZHOU Xin-chun, SHI Lan-fang, HAN Xiang-lin, MO Jia-qi. Homotopic mapping solitary traveling wave solutions for the disturbed BKK mechanism physical model[J].Chinese Physics B,2014,23(9): 090204.

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非线性扰动广义NNV系统的孤立子渐近行波解

doi: 10.3879/j.issn.1000-0887.2015.09.011

作者简介:
史娟荣(1981—), 女，安徽宣城人, 副教授, 硕士（E-mail: ahjdshjr@126.com）;莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

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Asymptotic Travelling Wave Soliton Solutions for Nonlinear Disturbed Generalized NNV Systems

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留言板

非线性扰动广义NNV系统的孤立子渐近行波解

doi: 10.3879/j.issn.1000-0887.2015.09.011

作者简介: 史娟荣(1981—), 女，安徽宣城人, 副教授, 硕士（E-mail: ahjdshjr@126.com）;莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).

计量

出版历程

Asymptotic Travelling Wave Soliton Solutions for Nonlinear Disturbed Generalized NNV Systems

计量

出版历程

目录

作者简介:
史娟荣(1981—), 女，安徽宣城人, 副教授, 硕士（E-mail: ahjdshjr@126.com）;莫嘉琪(1937—)，男，浙江德清人，教授(通讯作者. E-mail: mojiaqi@mail.ahnu.edu.cn).