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Based on the auxiliary equation method, the nonlinear superposition formula for the solutions of the second kind of elliptic equation is proposed. It is also used to construct the infinite sequence of new exact solutions to the generalized Boussinesq equation with the aid of symbolic computation system Mathematica. The infinite sequences of exact solutions include the Jacobi elliptic function infinite sequence solutions, the solitary wave infinite sequence solutions and the triangular function infinite sequence solutions. And the method is of significance to seek infinite sequence exact solutions to other nonlinear evolution equations.
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Keywords:
- nonlinear superposition formula /
- auxiliary equation method /
- Jacobi elliptic function /
- infinite sequence exact solution
[1] Parkes E J,Duffy B R 1996Comput. Phys. Commun. 98 288
[2] Wang M L 1995 Phys. Lett.A 199169
[3] Sirendaoreji,Sun J2003 Phys. Lett.A309387
[4] Fu Z T, Liu S D, Liu S K 2003Commun. Theor. Phys. (Beijing,China) 39531
[5] Zhao X Q,Zhi H Y , Zhang H Q 2006 Chin. Phys.15 2202
[6] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[7] Zhang L,Zhang L F, Li C Y2008 Chin. Phys.B 17 403
[8] Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[9] Li H M2005 Chin. Phys. 14251
[10] Zhu J M,Zheng C , Ma Z Y 2004 Chin. Phys. 132008
[11] Taogetusang,Sirendaoerji 2006 Chin. Phys. 152809
[12] Wu H Y,Zhang L,Tan Y K, Zhou X T 2008 Acta Phys. Sin. 57 3312(in Chinese)[吴海燕、张 亮、谭言科、周小滔 2008 物理学报57 3312]
[13] Gao L, Xu W,Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860(in Chinese)[高 亮、徐 伟、唐亚宁、申建伟 2007 物理学报56 1860]
[14] He F,Guo Q B,Liu L 2007ActaPhys. Sin. 56 4326(in Chinese)[贺 锋、郭启波、刘 辽 2007 物理学报56 4326]
[15] Wu Y Q 2008Acta Phys. Sin. 575390(in Chinese)[吴勇旗 2008 物理学报57 5390]
[16] Xu G Q,Li Z B 2003 Acta Phys. Sin. 521848(in Chinese)[徐桂琼、李志斌 2003 物理学报52 1848]
[17] Zhang S Q,Li Z B 2003Acta Phys. Sin. 52 1067(in Chinese)[张善卿、李志斌 2003 物理学报52 1067]
[18] Wang Z,Li D S,Lu H F,Zhang H Q2005Chin. Phys.142158
[19] Ma S H,Wu X H,Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11(inChinese) [马松华、 吴小红、 方建平、 郑春龙 2008 物理学报 57 11]
[20] Ma S H,Fang J P,Zheng C L2008 Chin. Phys. B172767
[21] Sirendaoerji2003J. Modern. Phys.C 14 1075
[22] PanJ T, Gong L X 2007 Acta Phys. Sin. 565585(in Chinese)[潘军廷、 龚伦训 2007 物理学报 56 5585]
[23] Chen Y,Li B 2004 Commun. Theor. Phys.(Beijing,China) 41 1
[24] Liu C S 2005Acta Phys. Sin. 54 4506(in Chinese)[刘成仕 2005 物理学报 544506]
[25] Li D S, Zhang H Q 2003 Acta Phys. Sin. 521569(in Chinese)[李德生、 张鸿庆 2003 物理学报 521569]
[26] Lu D C,Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617(in Chinese)[卢殿臣、 烘宝剑、 田立新 2006 物理学报 555617]
[27] Mao J J, Yang J R 2005Acta Phys. Sin. 54 4999(in Chinese)[毛杰健、 杨建荣 2005 物理学报 54 4999]
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[1] Parkes E J,Duffy B R 1996Comput. Phys. Commun. 98 288
[2] Wang M L 1995 Phys. Lett.A 199169
[3] Sirendaoreji,Sun J2003 Phys. Lett.A309387
[4] Fu Z T, Liu S D, Liu S K 2003Commun. Theor. Phys. (Beijing,China) 39531
[5] Zhao X Q,Zhi H Y , Zhang H Q 2006 Chin. Phys.15 2202
[6] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[7] Zhang L,Zhang L F, Li C Y2008 Chin. Phys.B 17 403
[8] Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[9] Li H M2005 Chin. Phys. 14251
[10] Zhu J M,Zheng C , Ma Z Y 2004 Chin. Phys. 132008
[11] Taogetusang,Sirendaoerji 2006 Chin. Phys. 152809
[12] Wu H Y,Zhang L,Tan Y K, Zhou X T 2008 Acta Phys. Sin. 57 3312(in Chinese)[吴海燕、张 亮、谭言科、周小滔 2008 物理学报57 3312]
[13] Gao L, Xu W,Tang Y N, Shen J W 2007 Acta Phys. Sin. 56 1860(in Chinese)[高 亮、徐 伟、唐亚宁、申建伟 2007 物理学报56 1860]
[14] He F,Guo Q B,Liu L 2007ActaPhys. Sin. 56 4326(in Chinese)[贺 锋、郭启波、刘 辽 2007 物理学报56 4326]
[15] Wu Y Q 2008Acta Phys. Sin. 575390(in Chinese)[吴勇旗 2008 物理学报57 5390]
[16] Xu G Q,Li Z B 2003 Acta Phys. Sin. 521848(in Chinese)[徐桂琼、李志斌 2003 物理学报52 1848]
[17] Zhang S Q,Li Z B 2003Acta Phys. Sin. 52 1067(in Chinese)[张善卿、李志斌 2003 物理学报52 1067]
[18] Wang Z,Li D S,Lu H F,Zhang H Q2005Chin. Phys.142158
[19] Ma S H,Wu X H,Fang J P, Zheng C L 2008 Acta Phys. Sin. 57 11(inChinese) [马松华、 吴小红、 方建平、 郑春龙 2008 物理学报 57 11]
[20] Ma S H,Fang J P,Zheng C L2008 Chin. Phys. B172767
[21] Sirendaoerji2003J. Modern. Phys.C 14 1075
[22] PanJ T, Gong L X 2007 Acta Phys. Sin. 565585(in Chinese)[潘军廷、 龚伦训 2007 物理学报 56 5585]
[23] Chen Y,Li B 2004 Commun. Theor. Phys.(Beijing,China) 41 1
[24] Liu C S 2005Acta Phys. Sin. 54 4506(in Chinese)[刘成仕 2005 物理学报 544506]
[25] Li D S, Zhang H Q 2003 Acta Phys. Sin. 521569(in Chinese)[李德生、 张鸿庆 2003 物理学报 521569]
[26] Lu D C,Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617(in Chinese)[卢殿臣、 烘宝剑、 田立新 2006 物理学报 555617]
[27] Mao J J, Yang J R 2005Acta Phys. Sin. 54 4999(in Chinese)[毛杰健、 杨建荣 2005 物理学报 54 4999]
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