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用近年来提出的(G'/G)展开法首次尝试了对变系数非线性发展方程的求解, 并以两类变系数非线性KdV方程为例,且成功得到了新的精确解. 实践证明: (G'/G)展开法不仅适用于常系数非线性发展方程, 而且还很好地适用于变系数非线性方程,具有广泛的应用前景.
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关键词:
- (G'/G)展开法 /
- 变系数非线性KdV方程 /
- 精确解
In this paper, the (G'/G)-expansion method is used to solve the two kinds of nonlinear KdV equations with variable coefficients for the first time. And some new exact solutions are obtained successfully. It is proved that the (G'/G)-expansion method is not only appropriate for solving nonlinear evolution equations with constant coefficients but also excellently applicable to the nonlinear evolution equations with variable coefficients, and it also has a broad application prospect.-
Keywords:
- the (G'/G)-expansion method /
- nonlinear KdV equation with variable coefficients /
- exact solutions
[1] Liu S S, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923 (in Chinese) [刘式适, 付遵涛, 刘式达, 赵强 2002 51 1923]
[2] Liu C S 2005 Acta Phys. Sin. 54 4506 (in Chinese) [刘成仕 2005 54 4506]
[3] Yang X L, Tang J S 2007 J. Hunan Univ. 34 72 (in Chinese) [杨先林, 唐驾时 2007 湖南大学学报 34 72]
[4] Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆 2003 52 1569]
[5] Zhang J F, Chen F Y 2001 Acta Phys. Sin. 50 1648 (in Chinese) [张解放, 陈芳跃 2001 50 1648]
[6] Cai G L, Ling X D, Wang Q C 2008 J. College Math. 24 26 (in Chinese) [蔡国梁, 凌旭东, 王庆超 2008 大学数学 24 26]
[7] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 56 5049]
[8] Zhou Y B, Wang M L, Wang F, Miao T D 2004 J. Lanzhou Univ. 40 1
[9] Ao T G 2007 J. Inner Monglia Univ. 38 597 (in Chinese) [敖特根 2007 内蒙古大学学报 38 597]
[10] Wang M L, Li X Z, Zhang J L 2008 J. Phys. Lett. A 372 417
[11] Feng Q H, Meng F W, Zhang Y M 2011 Chin. Phys. B 20 120201
[12] Zhang J, Wei X L, Lu Y J 2008 J. Phys. Lett. A 372 3653
[13] Filiz T, Ahmet B 2010 Chin. Phys. B 20 040203
[14] Li E Q, Wang M L 2008 J. Henan Sci. Technol. Univ. 29 80 (in Chinese) [李二强, 王明亮 2008 河南科技大学学报 29 80]
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[1] Liu S S, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 1923 (in Chinese) [刘式适, 付遵涛, 刘式达, 赵强 2002 51 1923]
[2] Liu C S 2005 Acta Phys. Sin. 54 4506 (in Chinese) [刘成仕 2005 54 4506]
[3] Yang X L, Tang J S 2007 J. Hunan Univ. 34 72 (in Chinese) [杨先林, 唐驾时 2007 湖南大学学报 34 72]
[4] Li D S, Zhang H Q 2003 Acta Phys. Sin. 52 1569 (in Chinese) [李德生, 张鸿庆 2003 52 1569]
[5] Zhang J F, Chen F Y 2001 Acta Phys. Sin. 50 1648 (in Chinese) [张解放, 陈芳跃 2001 50 1648]
[6] Cai G L, Ling X D, Wang Q C 2008 J. College Math. 24 26 (in Chinese) [蔡国梁, 凌旭东, 王庆超 2008 大学数学 24 26]
[7] Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 56 5049]
[8] Zhou Y B, Wang M L, Wang F, Miao T D 2004 J. Lanzhou Univ. 40 1
[9] Ao T G 2007 J. Inner Monglia Univ. 38 597 (in Chinese) [敖特根 2007 内蒙古大学学报 38 597]
[10] Wang M L, Li X Z, Zhang J L 2008 J. Phys. Lett. A 372 417
[11] Feng Q H, Meng F W, Zhang Y M 2011 Chin. Phys. B 20 120201
[12] Zhang J, Wei X L, Lu Y J 2008 J. Phys. Lett. A 372 3653
[13] Filiz T, Ahmet B 2010 Chin. Phys. B 20 040203
[14] Li E Q, Wang M L 2008 J. Henan Sci. Technol. Univ. 29 80 (in Chinese) [李二强, 王明亮 2008 河南科技大学学报 29 80]
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