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Approximate solutions of nonlinear PDEs by the invariant expansion |
| Wu Jiang-Long (吴江龙)a, Lou Sen-Yue (楼森岳)b |
a Faculty of Science, Ningbo University, Ningbo 315211, China;
b Center of Nonlinear Science, Ningbo University, Ningbo 315211, China |
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Abstract It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear system. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as Korteweg-de Vries (KdV) equation with fifth-order dispersion term, perturbed fourth-order KdV equation, KdV-Burgers equation, and Boussinesq type of equation.
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Received: 28 April 2012
Revised: 20 June 2012
Accepted manuscript online:
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PACS:
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02.30.Jr
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(Partial differential equations)
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47.10.ab
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(Conservation laws and constitutive relations)
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02.30.Ik
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(Integrable systems)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11175092), Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201017148), and K. C. Wong Magna Fund in Ningbo University. |
Corresponding Authors:
Wu Jiang-Long
E-mail: wjlazxm@sina.com;375516508@qq.com
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Cite this article:
Wu Jiang-Long (吴江龙), Lou Sen-Yue (楼森岳) Approximate solutions of nonlinear PDEs by the invariant expansion 2012 Chin. Phys. B 21 120204
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| [1] |
Weiss J, Tabor M and Carnevale G 1983 J. Math. Phys. 24 1405
|
| [2] |
Nucci M C 1989 J. Phys. A: Math. Gen. 22 2897
|
| [3] |
Lou S Y and Xu J J 1998 J. Math. Phys. 39 5364
|
| [4] |
Zhang S L, Wu B and Lou S Y 2002 Phys. Lett. A 300 40
|
| [5] |
Zhang S L, Tang X Y and Lou S Y 2002 Commun. Theor. Phys. 38 513
|
| [6] |
Liang Z F and Tang X Y 2009 Phys. Lett. A 374 110
|
| [7] |
Conte R 1989 Phys. Lett. A 140 383
|
| [8] |
Cariello and Tabor M 1991 Physica D 53 59
|
| [9] |
Pickering A 1993 J. Phys. A: Math. Gen. 26 4395
|
| [10] |
Lou S Y 1998 Z. Naturforsch 53a 251
|
| [11] |
Ruan H Y 1999 Journal of Ningbo University 12 42
|
| [12] |
Tang X Y and Hu H C 2002 Chin. Phys. Lett. 19 1225
|
| [13] |
Zhang M X, Liu Q P, Wang J and Wu K 2008 Chin. Phys. B 17 10
|
| [14] |
Liu X Z 2010 Chin. Phys. B 19 080202
|
| [15] |
Li J M, Liang Z F and Tang X Y 2010 Chin. Phys. B 19 100205
|
| [16] |
Yang R S, Yao C M and Chen R X 2009 Chin. Phys. B 18 3736
|
| [17] |
Wang Y F, Lou S Y and Qian X M 2010 Chin. Phys. B 19 050202
|
| [18] |
Yao R X, Jiao X Y and Lou S Y 2009 Chin. Phys. B 18 1821
|
| [19] |
Wang H, Dong H H, Wang Y H and Wang X Z 2010 Chin. Phys. B 19 060202
|
| [20] |
Katuro S and Takeyasu K 1974 Prog. Theor. Phys. 51 1355
|
| [21] |
Wu B and Lou S Y 2002 Commun. Theor. Phys. 38 649
|
| [22] |
Jeffrey A and Mohamad M N B 1991 Wave Motion 14 369
|
| [23] |
Jun K C, Satsuma and D J Kaup 1977 J. Phys. Soc. Jpn. 43 692
|
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