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对(G'/G)展开法做了进一步的研究, 利用两次函数变换将二阶非线性辅助方程的求解问题转化为一元二次代数方程与Riccati方程的求解问题. 借助Riccati方程的Bcklund变换及解的非线性叠加公式获得了辅助方程的无穷序列解. 这样, 利用(G'/G)展开法可以获得非线性发展方程的无穷序列解, 这一方法是对已有方法的扩展, 与已有方法相比可获得更丰富的无穷序列解. 以(2+1)维改进的Zakharov-Kuznetsov方程为例得到了它的无穷序列新精确解. 这一方法可以用来构造其他非线性发展方程的无穷序列解.
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关键词:
- (G' /
- /G)展开法 /
- 改进的Zakharov-Kuznetsov方程 /
- 精确解
The (G'/G)-expansion method is further studied, the solution to the second-order nonlinear auxiliary equation is changed into solving of one unknown quadratic equation and Riccati equation by two function transformations. An infinite sequence solution of auxiliary equation is obtained with the help of Bcklund transformation of Riccati equation and nonlinear superposition formula of the solution. In this way, the infinite sequence solution to the nonlinear evolution equation can be obtained by the (G'/G)-expansion method, this method is an extension of existing methods, which can get more infinite series solutions. Take the (2+1)-dimensional Zakharov-Kuznetsov modified equal width equation as an example to obtain the new infinite sequence solution. This method can be used to get the infinite sequence solution to other nonlinear evolution equations.-
Keywords:
- (G' /
- /G)-expansion method /
- Zakharov-Kuznetsov modified equal width equation /
- exact solutions
[1] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Phys. Lett. A 289 69
[2] Zhang S 2007 Phys. Lett. A 368 470
[3] Wu J P 2011 Chin. Phys. Lett. 28 060207
[4] Zuo J M, Zhang Y M 2011 Chin. Phys. B 20 010205
[5] Li Z B, Zhang S Q 1997 Acta Math. Sin. 17 81 (in Chinese) [李志斌, 张善卿 1997 数学物理学报 17 81]
[6] Wang M L 1995 Acta Lett. A 199 169
[7] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[8] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[9] Chen H T, Zhang H Q 2004 Chaos, Soliton. Fract. 20 765
[10] Alam M N, Akbar M A, Mohyud-Din S T 2014 Chin. Phys. B 23 020203
[11] Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[12] Gepreel K A, Omran S 2012 Chin. Phys. B 21 110204
[13] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417
[14] Bekir A, Ayhan B, Özer M N 2013 Chin. Phys. B 22 010202
[15] Shehata A R 2010 Appl. Math. Comput. 217 1
[16] Zayed E M E 2009 J. Appl. Math. Comput. 30 89
[17] Inca M, Ulutas E, Biswasc A 2013 Chin. Phys. B 22 060204
[18] Zhao Y L, Liu Y P, Li Z B 2010 Chin. Phys. B 19 030306
[19] Taogetusang 2013 Acta Phys. Sin. 62 070202 (in Chinese) [套格图桑 2013 物理学报 62 070202]
[20] Taogetusang 2013 Acta Phys. Sin. 62 210201 (in Chinese) [套格图桑 2013 物理学报 62 210201]
[21] Yi L N, Taogetusang 2014 Acta Phys. Sin. 63 030201 (in Chinese) [伊丽娜, 套格图桑 2014 物理学报 63 030201]
[22] Khalique C M 2011 Math. Comput. Model. 54 184
[23] Wazwaz A M 2005 Int. J. Comput. Math. 82 699
[24] Wazwaz A M 2006 Commun. Nonlinear Sci. Numer. Simul. 11 148
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[1] Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Phys. Lett. A 289 69
[2] Zhang S 2007 Phys. Lett. A 368 470
[3] Wu J P 2011 Chin. Phys. Lett. 28 060207
[4] Zuo J M, Zhang Y M 2011 Chin. Phys. B 20 010205
[5] Li Z B, Zhang S Q 1997 Acta Math. Sin. 17 81 (in Chinese) [李志斌, 张善卿 1997 数学物理学报 17 81]
[6] Wang M L 1995 Acta Lett. A 199 169
[7] Shi L F, Chen C S, Zhou X C 2011 Chin. Phys. B 20 100507
[8] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[9] Chen H T, Zhang H Q 2004 Chaos, Soliton. Fract. 20 765
[10] Alam M N, Akbar M A, Mohyud-Din S T 2014 Chin. Phys. B 23 020203
[11] Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[12] Gepreel K A, Omran S 2012 Chin. Phys. B 21 110204
[13] Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417
[14] Bekir A, Ayhan B, Özer M N 2013 Chin. Phys. B 22 010202
[15] Shehata A R 2010 Appl. Math. Comput. 217 1
[16] Zayed E M E 2009 J. Appl. Math. Comput. 30 89
[17] Inca M, Ulutas E, Biswasc A 2013 Chin. Phys. B 22 060204
[18] Zhao Y L, Liu Y P, Li Z B 2010 Chin. Phys. B 19 030306
[19] Taogetusang 2013 Acta Phys. Sin. 62 070202 (in Chinese) [套格图桑 2013 物理学报 62 070202]
[20] Taogetusang 2013 Acta Phys. Sin. 62 210201 (in Chinese) [套格图桑 2013 物理学报 62 210201]
[21] Yi L N, Taogetusang 2014 Acta Phys. Sin. 63 030201 (in Chinese) [伊丽娜, 套格图桑 2014 物理学报 63 030201]
[22] Khalique C M 2011 Math. Comput. Model. 54 184
[23] Wazwaz A M 2005 Int. J. Comput. Math. 82 699
[24] Wazwaz A M 2006 Commun. Nonlinear Sci. Numer. Simul. 11 148
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