近年来,变系数非线性发展方程受到越来越多的关注. 2008年王明亮等提出了一种新的方法,即(G’/G)展开法.将(G’/G)展开法首次尝试应用到变系数非线性发展方程中,并以广义变系数Burgers方程为例,成功得到了在系数满足一定条件时新的精确解；又尝试将该展开法进行新的扩展,再一次对广义变系数Burgers方程求解,又成功得到了一些新解.实践证明,该展开法不仅易于求解常系数非线性发展方程,而且对变系数非线性发展方程仍很高效、简洁、实用,并且具有广泛的应用前景.
参考文献
| [1] | Li Zhibin.Travelling Wave Solutions of Nonlinear Mathematical and Physical Equations(非线性数学物理方法的行波解)[M].Beijing:Science Press,2006 (in Chinese). |
| [2] | Lou Senyue,Tang Xiaoyan.Method of Nonlinear Mathematics and Physics(非线性数学物理方法)[M].Beiiing:Science Press,2006 (in Chinese). |
| [3] | Liu Shishi,Liu Shida.Nonlinear Equations of Physics(物理学中的非线性方程)[M].Beijing:Peking University Press,2000 (in Chinese). |
| [4] | Guo Yucui.Introduction to Nonlinear Partial Differential Equations(非线性偏微分方程引论)[M].Beijing:Tsinghua University Press,2008 (in Chinese). |
| [5] | Wang Mingliang,Li Xiangzheng,Zhang Jingliang.The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics[J].Phys.Lett.A,2008,372:417-423. |
| [6] | Bekir A.Application of the (G'/G)-expansion method for nonlinear evolution equations[J].Phys.Lett.A,2008,372:3400-3406. |
| [7] | Zhang Jiao,Wei Xiaoli,Lu Yongjie.A generalized (G'/G)-expansion method and its applications[J].Phys.Lett.A,2008,372:3653-3658. |
| [8] | Zhang Sheng,Tong Jinglin,Wang Wei.A generalized (G'/G)-expansion method for the mKdV equation with variable coefficients[J].Phys.Lett.A,2008,372:2254-2257. |
| [9] | Siddique I,Rizvi S T R,Batool F.New exact travelling wave solutions of nonlinear evolution equations[J].International Journal of Nonlinear Science,2010,9(1):12-18. |
| [10] | Zhou Yubin,Wang Mingliang,Wang Fan,et al.Auto-Backlund transformation and multi-soliton solutions to a coupled KdV equations with variable coefficients[J].Journal of Lanzhou University (Natural Sciences) (兰州理工大学学报(自然科学版)),2004,40(3):03-10(in Ghinese). |
| [11] | Pang Jing,Bian Chunquan,Chao Lu.A new auxiliary equation method of solving the KdV equation[J].Applied Mathematics and Mechanics,2010,31(7):927-936. |
| [12] | Wazwaz A M.The tanh method for travelling wave solutions of nonlinear equations[J].Appl.Math.Comput.,2004,154(3):713-723. |
| [13] | Zhang Sheng.Application of Exp-function method to high-dimensional nonlinear evolution equation[J].Chaos Solitons Fractals,2006,014-016. |
| [14] | Shi Yuren,Lii Kepu,Duan Wenshan,et al.Exact solution to Burgers equation with variable coefficient[J].Journal of Lanzhou University (Natural Sciences)(兰州理工大学学报(自然科学版)),2005,41(4):107-111 (in Chinese). |
| [15] | Shi Yuren,Wang Yinghai,Yang Hongjuan,et al.Exact solutions of generalized Burgers ' s equation with variable coefficient[J].Journal of East China Normal University(Natural Sciences)(华东师范大学学报(自然科学版)),2006,5:27-33 (in Chinese). |
| [16] | Li Erqiang,et al.(G'/G)-method and travelling wave solutions to compound KdV-Burgers quation[J].Journal of Henan University of Science and Technology (Natural Science)(河南科技大学学报(自然科学版)),2008,29(5):80-85(in Chinese). |
| [17] | Zhang Jinliang,Li Xiangzheng,Wang Mingliang,et al.New exact solution to Burgers equation with variable coefficient[J].Journal of Henan University of Science and Technology (Natural Science)(河南科技大学学报(自然科学版)),2004,24(1):108-110 (in Chinese). |
| [18] | Xu Liping,Cao Hongyan.Exact solution to Burgers equation with variable coefficient[J].Journal of Qingdao University of Science and Technology(青岛科技大学学报),2006,27(2):186-188(in Chinese). |
| [19] | Taogetusang,Sirendaoerji.Jacobi elliptic function exact solutions of sine-Gordon equation[J].Chinese Journal of Quantum Electronics(量子电子学报),2009,26(3):278-287 (in Chinese). |
| [20] | Sirendaoerji.Auxiliary equation method and soution wave solutions to nonlinear evolution equations[J].Journal of Inner Mongolia Normal University (Natural Science Edition)(内蒙古师范大学学报(自然科学版)),2003,35(2):127-131 (in Chinese). |
| [21] | Taogetusang,Sirendaoerji.New solitary wave solutions of the combined KdV equation with the variable coefficients[J].Chinese Journal of Quantum Electronics(量子电子学报),2009,26(2):148-154(in Chinese). |
上一张
下一张
上一张
下一张
计量
- 下载量()
- 访问量()
文章评分
- 您的评分：
-
10%
-
20%
-
30%
-
40%
-
50%