应用全新G′/（G+G′）展开方法求解广义非线性Schrödinger方程和耦合非线性Schrödinger方程组

石兰芳; 聂子文

doi:10.21656/1000-0887.370269

应用全新G′/（G+G′）展开方法求解广义非线性Schrödinger方程和耦合非线性Schrödinger方程组

doi: 10.21656/1000-0887.370269

南京信息工程大学数学与统计学院, 南京 210044

基金项目: 国家自然科学基金(11202106;61201444)；教育部高等学校博士学科点专项科研基金(20123228120005) ；江苏省“信息与通信工程”优势学科建设基金；江苏省自然科学基金(BK20131005)；江苏省青蓝工程和江苏省高校自然科学研究基金(13KJB170016)

详细信息

作者简介:
石兰芳（1976—），女，副教授，博士，硕士生导师（通讯作者. E-mail: shilf108@163.com）;聂子文（1993—），男，硕士生（E-mail: niezw109@163.com）.

中图分类号: O175.29
计量
- 文章访问数: 1426
- HTML全文浏览量: 257
- PDF下载量: 697
- 被引次数: 0
出版历程
- 收稿日期: 2016-09-05
- 修回日期: 2017-03-21
- 刊出日期: 2017-05-15

Solutions to the Nonlinear Schrödinger Equation and Coupled Nonlinear Schrödinger Equations With a New G′/（G+G′）-Expansion Method

College of Mathematics and Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R.China

Funds: The National Natural Science Foundation of China(11202106; 61201444)

摘要

摘要: 研究了一种全新的G′/（G+G′）展开方法，并应用这种方法讨论了广义非线性Schrödinger方程和一类耦合非线性Schrödinger方程组新形式的精确解，包括双曲余切函数解、余切函数解和有理函数解.全新G′/（G+G′）展开方法不但直接而有效地求出方程的新精确解，而且扩大了解的范围，这种新方法对于研究偏微分方程具有广泛的应用意义.
- 全新G′/（G+G′）展开方法 /
- 广义非线性Schrödinger方程 /
- 耦合非线性Schrödinger方程组 /
- 精确解
Abstract: A new G′/（G+G′）-expansion method was proposed. Exact solutions to a class of Schrödinger equations and coupled nonlinear Schrödinger equations were obtained with this new method. The solutions can be expressed with the hyperbolic cotangent functions, the cotangent functions and the rational functions. This new G′/（G+G′）-expansion method not only help gets new exact solutions to the equations directly and effectively, but also expands the scope of the solutions. This new method promises a very wide range of application for the study of related partial differential equations.
- new G′/（G+G′）-expansion method /
- generalized nonlinear Schrödinger equation /
- coupled nonlinear Schrödinger equations /
- exact solution

HTML全文

参考文献(30)

[1]	Rogers C, Shadwick W F. Backlund Transformations and Their Applications [M]. New York: Academic Press, 1982.
[2]	Hirota R. Exact solution of the Korteweg-de-Vries equation for multiple collisions of solitons[J]. Physical Review Letters,1971,27(18): 1192-1194.
[3]	Malfliet W. Solitary wave solutions of nonlinear wave equations[J]. American Journal of Physics,1992,60(7): 650-654.
[4]	Wazwaz A M. The tanh-coth method for solitons and kink solutions for nonlinear parabolic equations[J]. Applied Mathematics and Computation,2007,188(2): 1467-1475.
[5]	Abdou M A. The extended F -expansion method and its application for a class of nonlinear evolution equations[J].Chaos, Solitons & Fractals,2007,31(1): 95-104.
[6]	HE Ji-huan, WU Xu-hong. Exp-function method for nonlinear wave equations[J]. Chaos, Solitons & Fractals,2006,30(3): 700-708.
[7]	Ablowitz M J, Clarkson P A. Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform [M]. Cambridge: Cambridge University Press, 1991.
[8]	石兰芳, 汪维刚, 莫嘉琪. 高维扰动破裂孤子方程行波解的渐近解法[J]. 应用数学, 2014,27(2): 317-321.(SHI Lan-fang, WANG Wei-gang, MO Jia-qi. Asymptotic solving method of traveling solution for higher dimensional disturbed breaking solution equation[J]. Mathematica Applicata,2014,27(2): 317-321.(in Chinese))
[9]	SHI Lan-fang, CHEN Cai-sheng, ZHOU Xian-chun. The extended auxiliary equation method for the KdV equation with variable coefficients[J]. Chinese Physics B,2011,20(10): 100507-1-100507-5.
[10]	许丽萍, 阮苗, 张金良. 光纤中两个高阶变系数薛定谔方程的精确解[J]. 工程数学学报, 2008,25(6): 1044-1050.(XU Li-ping, RUAN Miao, ZHANG Jin-liang. Exact wave solutions of two higher order nonlinear Schrdinger equations with variable-coefficients[J]. Chinese Journal of Engineering Mathematics,2008,25(6): 1044-1050.(in Chinese))
[11]	陈娟. 一类非线性Schrdinger方程的Jacobi椭圆函数周期解[J]. 应用数学学报, 2014,37(4): 656-661.(CHEN Juan. Periodic wave solutions expressed by Jacobi elliptic functions for a class of nonlinear Schrdinger equation[J]. Acta Mathematica Applicatae Sinica,2014,37(4): 656-661.(in Chinese))
[12]	WANG Ming-liang, LI Xiang-zheng, ZHANG Jin-liang. The G′/G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics[J]. Physics Letters A,2008,372(4): 417-423.
[13]	Arbabi S, Najafi M. Exact solitary wave solutions of the complex nonlinear Schrdinger equations[J]. Optik,2016,127(11): 4682-4688.
[14]	DENG Xi-jun. Exact peaked wave solution of CH- γ equation by the first-integral method[J]. Applied Mathematics and Computation,2008,206(2): 321-326.
[15]	石兰芳, 莫嘉琪. 用广义变分迭代理论求一类相对转动动力学方程的解[J]. 物理学报, 2013,62(4): 040203-1-040203-6.(SHI Lan-fang, MO Jia-qi. Solution of a class of rotational relativistic rotation dynamic equation using the generalized variational iteration theory[J]. Acta Physica Sinica,2013,62(4): 040203-1-040203-6.(in Chinese))
[16]	石兰芳, 林万涛, 林一骅, 等. 一类非线性方程类孤波的近似解法[J]. 物理学报, 2013,62(1): 010201-1-010201-5.(SHI Lan-fang, LIN Wan-tao, LIN Yi-hua, et al. Approximate method of solving solitary-like wave for a class of nonlinear equation[J]. Acta Physica Sinica,2013,62(1): 010201-1-010201-5.(in Chinese))
[17]	石兰芳, 莫嘉琪. 一类扰动非线性发展方程类孤子同伦近似解析解[J]. 物理学报, 2009,58(12): 8123-8126.(SHI Lan-fang, MO Jia-qi. Soliton-like homotopic approximate analytic solution for a class of disturbed nonlinear evolution equation[J]. Acta Physica Sinica,2009,58(12): 8123-8126.(in Chinese))
[18]	冯依虎, 石兰芳, 许永红, 等. 一类大气尘埃等离子体扩散模型研究[J]. 应用数学和力学, 2015,36(6): 639-650.(FENG Yi-hu, SHI Lan-fang, XU Yong-hong, et al. Study on a class of diffusion models for dust plasma in atmosphere[J]. Applied Mathematics and Mechanics,2015,36(6): 639-650.(in Chinese))
[19]	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. Solutions to a class of nonlinear strong-damp disturbed evolution equations[J]. Applied Mathematics and Mechanics,2014,35(9): 1046-1054.(in Chinese))
[20]	石兰芳, 欧阳成, 陈丽华, 等. 一类大气等离子体反应扩散模型的解法[J]. 物理学报, 2012,61(5): 050203-1-050203-6.(SHI Lan-fang, OUYANG Cheng, CHEN Li-hua, et al. Solving method of a class of reactive diffusion model for atmospheric plasmas[J]. Acta Physica Sinica,2012,61(5): 050203-1-050203-6.(in Chinese))
[21]	石兰芳, 林万涛, 温朝辉, 等. 一类奇摄动Robin问题的内部冲击波解[J]. 应用数学学报, 2013,36(1): 108-114.(SHI Lan-fang, LIN Wan-tao, WEN Zhao-hui, et al. Internal shock solution for a class of singularly perturbed Robin problems[J]. Acta Mathematica Applicatae Sinica,2013,36(1): 108-114.(in Chinese))
[22]	张善卿, 李志斌. 非线性耦合Schrdinger-KdV方程组新的精确解析解[J]. 物理学报, 2002,51(10): 2197-2201.(ZHANG Shan-qing, LI Zhi-bin. New explicit exact solutions to nonlinearly coupled Schrdinger-KdV equations[J]. Acta Physica Sinica,2002,51(10): 2197-2201.(in Chinese))
[23]	阮航宇, 李慧军. 用推广的李群约化法求解非线性薛定谔方程[J]. 物理学报, 2005,54(3): 996-1001.(RUAN Hang-yu, LI Hui-jun. Solution of the nonlinear Schrdinger equation using the generalized Lie group reduction method[J]. Acta Physica Sinica,2005,54(3): 996-1001.(in Chinese))
[24]	Najafi M, Arbabi S. Exact solutions of five complex nonlinear Schrdinger equations by semi-inverse variational principle[J]. Communications in Theoretical Physics,2014,62(3): 301-307.
[25]	Najafi M, Arbabi S. Traveling wave solutions for nonlinear Schrdinger equations[J]. Optik,2015,126(23): 3992-3997.
[26]	张解放, 徐昌智, 何宝钢. 变量分离法与变系数非线性薛定谔方程的求解探索[J]. 物理学报，2004,53(11): 3652-3656.(ZHANG Jie-fang, XU Chang-zhi, HE Bao-gang. The variable separation approach and study on solving the variable-coefficient nonlinear Schrdinger equation[J]. Acta Physica Sinica,2004,53(11): 3652-3656.(in Chinese))
[27]	ZHAO Dun, LUO Hong-gang, WANG Shun-jin, et al. A direct truncation method for finding abundant exact solutions and application to the one-dimensional higher-order Schr?dinger equation[J]. Chaos, Solitons & Fractals,2005,24(2): 533-547.
[28]	张金良, 李向正, 王明亮. 两个非线性耦合方程组的复tanh函数解[J]. 工程数学学报, 2005,22(4): 725-728.(ZHANG Jin-liang, LI Xiang-zhang, WANG Ming-liang. The complex tanh-function solutions to two nonlinear coupled evolution equations[J]. Chinese Journal of Engineering Mathematics,2005,22(4): 725-728.(in Chinese))
[29]	TIAN Bao, GAO Yi-tian. Variable-coefficient higher-order nonlinear Schrdinger model in optical fibers: new transformation with Burstons, brightons and symbolic computation[J]. Physics Letters A,2006,359(3): 241-248.
[30]	Baboiu D M, Stegeman G I, Torner L. Interaction of one-dimensional bright solitary waves in quadratic media[J]. Optics Letters,1995,20(22): 2282-2284.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 1426
HTML全文浏览量: 257
PDF下载量: 697
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

应用全新G′/（G+G′）展开方法求解广义非线性Schrödinger方程和耦合非线性Schrödinger方程组

doi: 10.21656/1000-0887.370269

作者简介:
石兰芳（1976—），女，副教授，博士，硕士生导师（通讯作者. E-mail: shilf108@163.com）;聂子文（1993—），男，硕士生（E-mail: niezw109@163.com）.

计量

Solutions to the Nonlinear Schrödinger Equation and Coupled Nonlinear Schrödinger Equations With a New G′/（G+G′）-Expansion Method

计量

目录

留言板

应用全新G′/（G+G′）展开方法求解广义非线性Schrödinger方程和耦合非线性Schrödinger方程组

doi: 10.21656/1000-0887.370269

作者简介: 石兰芳（1976—），女，副教授，博士，硕士生导师（通讯作者. E-mail: shilf108@163.com）;聂子文（1993—），男，硕士生（E-mail: niezw109@163.com）.

计量

出版历程

Solutions to the Nonlinear Schrödinger Equation and Coupled Nonlinear Schrödinger Equations With a New G′/（G+G′）-Expansion Method

计量

出版历程

目录

作者简介:
石兰芳（1976—），女，副教授，博士，硕士生导师（通讯作者. E-mail: shilf108@163.com）;聂子文（1993—），男，硕士生（E-mail: niezw109@163.com）.