[1]吴丽华,赵倩.耦合Burgers方程的Darboux变换及精确解[J].华侨大学学报(自然科学版),2017,38(4):585-590.[doi:10.11830/ISSN.1000-5013.201704026]
　WU Lihua,ZHAO Qian.Darboux Transformation and Exact Solutions to Coupled Burgers Equation[J].Journal of Huaqiao University(Natural Science),2017,38(4):585-590.[doi:10.11830/ISSN.1000-5013.201704026]
点击复制

耦合Burgers方程的Darboux变换及精确解()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第38卷
期数:
2017年第4期
页码:
585-590
栏目:
出版日期:
2017-07-10

文章信息/Info

Title:
Darboux Transformation and Exact Solutions to Coupled Burgers Equation
文章编号:
1000-5013(2017)04-0585-06
作者:
吴丽华;  赵倩
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
WU Lihua;  ZHAO Qian
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
耦合Burgers方程;  规范变换;  Darboux变换;  精确解
Keywords:
coupled Burgers equation;  gauge transformation;  Darboux transformation;  exact solutions
分类号:
O175
DOI:
10.11830/ISSN.1000-5013.201704026
文献标志码:
A
摘要:
通过引入与耦合Burgers方程相联系的3×3矩阵谱问题的规范变换,构造出耦合Burgers方程的一个Darboux变换,并由此得到了它的一些精确解.
Abstract:
A Darboux transformation of the coupled Burgers equation is constructed with the help of the gauge transformation of the associated 3×3 matrix spectral problems, from which we obtain some exact solutions of the coupled Burgers equation.

参考文献/References:

[1] ABLOWITZ M J,KAUP D J,NEWELL A C.The inverse scattering transform-Fourier analysis for nonlinear problems[J].Stud Appl Math,1974,53(4):249-315.
[2] ABLOWITZ M J,SEGUR H.Solitons and the inverse scattering transform[M].SIAM:Philadelphia,1981.
[3] HIROTA R.The direct method in soliton theory[M].Cambridge:Cambridge University Press,2004.
[4] ABLOWITZ M J,RAMANI A,SEGUR H.A connection between nonlinear evolution equations and ordinary differential equations of p-type Ⅰ[J].Math Phys,1980,21(4):715-721.
[5] ABLOWITZ M J,RAMANI A,SEGUR H.A connection between nonlinear evolution equations and ordinary differential equations of p-type Ⅱ[J].Math Phys,1980,21(5):1006-1015.
[6] NOVIKOV S P.The periodic problem for the Korteweg-de vries equation[J].Funct Anal Appl,1974,8(3):236-246.
[7] ITS A R, MATVEEV V B. Schrödinger operators with finite-gap spectrum and N-soliton solutions of the Korteweg-de Vries equation[J].Theor Math Phys,1975,23(1):51-68.
[8] MATVEEV V B,SALLE M A.Darboux transformation and solitons[J].Journal of Neurochemistry,1991,42(6):1667-1676.
[9] 谷超豪,胡和生,周子翔.孤立子理论中的达布变换及其几何应用[M].2版.上海:上海科学技术出版社,2005.
[10] GENG Xianguo,WANG Hui.A hierarchy of new nonlinear evolution equations and their bi-Hamiltonian structures[J].Chin Phys Lett,2014,31(7):5-8.

备注/Memo

备注/Memo:
收稿日期: 2016-11-22
通信作者: 吴丽华(1983-),女,副教授,博士,主要从事孤立子与可积系统的研究.E-mail:wulihua@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11401230); 福建省高校杰出青年科研人才培育计划项目(2015年度); 华侨大学中青年教师科技创新资助计划(ZQN-PY301)
更新日期/Last Update: 2017-07-20