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To seek new infinite sequence complexiton solutions to nonlinear evolution equations(NEE(s)), the formula of nonlinear superposition of the solutions and Bcklund transformation of Riccati equation are presented, and as an illusrative exapmle, the generalized Boussinesq equation is chosen to obtain new infinite sequence complexiton solutions with the aid of symbolic computation system Mathematica, which includes complexiton solutions of hyperbolic function, triangular function type with rational function and hyperbolic function with triangular function. The method is of significance to construct infinite sequence complexiton solutions to other NEEs.
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Keywords:
- nonlinear evolution equation /
- formula of nonlinear superposition /
- Riccati equation /
- infinite sequence exact solution
[1] Zhang L, Zhang L F, Li C Y2008Chin.Phys.B 17 403
[2] [3] [4] Wu H Y, Zhang L, Tan Y K, Zhou X T 2008Acta.Phys.Sin. 57 3312(in Chinese) [吴海燕、张 亮、谭言科、周小滔 2008 57 3312]
[5] [6] Gao L, Xu W, Tang Y N, Shen J W 2007Acta.Phys.Sin. 561860(in Chinese)[高 亮、徐 伟、唐亚宁、申建伟 2007 56 1860]
[7] Xu G Q, Li Z B 2003Acta.Phys.Sin. 521848(in Chinese)[徐桂琼、李志斌 2003 52 1848]
[8] [9] [10] Wang M L 1995 Phys.Lett. A 199 169
[11] [12] Wu Y Q 2008 Acta.Phys.Sin. 57 5390(in Chinese)[吴勇旗 2008 57 5390]
[13] [14] He F, Guo Q B, Liu L 2007 Acta.Phys.Sin. 56 4326(in Chinese)[贺 锋、郭启波、 刘 辽 2007 56 4326]
[15] Zhang S Q, Li Z B 2003Acta.Phys.Sin. 52 1067(in Chinese)[张善卿、李志斌 2003 52 1067]
[16] [17] Wang Z, Li D S,Lu H F,Zhang H Q2005 Chin.Phys. 14 2158
[18] [19] Parkes E J, Duffy B R 1996Comput.Phys.Commun. 98288
[20] [21] Sirendaoreji, Sun J 2003Phys. Lett.A309387
[22] [23] Fu Z T, Liu S D, Liu S K 2003Commun.Theor.Phys.(Beijing,China) 39 531
[24] [25] Zhao X Q, Zhi H Y, Zhang H Q 2006Chin.Phys. 15 2202
[26] [27] [28] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin.Phys. 12 825
[29] [30] Lu B, Zhang H Q 2008Chin.Phys.B 17 3974
[31] [32] Li H M 2005Chin.Phys. 14251
[33] [34] Zhu J M, Zheng C L, Ma Z Y 2004Chin.Phys. 132008
[35] Taogetusang, Sirendaoerji 2006 Chin.Phys. 15 2809
[36] [37] Pan J T, Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese)[潘军廷、龚伦训 2007 56 5585]
[38] [39] Sirendaoerji2003 J.Modern.Phys. C 14 1075
[40] [41] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta.Phys.Sin. 57 11(in Chinese) [马松华、 吴小红、 方建平、 郑春龙 2008 57 11]
[42] [43] [44] Ma S H,Fang J P,Zheng C L2008 Chin.Phys.B 172767
[45] [46] Chen Y, Li B 2004 Commun.Theor.Phys.(Beijing, China) 41 1
[47] [48] Liu C S 2005 Acta.Phys.Sin. 544506(in Chinese)[刘成仕 2005 544506]
[49] Li D S, Zhang H Q 2003 Acta.Phys.Sin. 521569(in Chinese)[李德生、张鸿庆 2003 521569]
[50] [51] [52] Lu D C, Hong B J, Tian L X2006 Acta.Phys.Sin. 555617(in Chinese)[卢殿臣、烘宝剑、田立新 2006 555617]
[53] [54] Mao J J, Yang J R2005Acta.Phys.Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[55] [56] Ma S H, Fang J P 2006Acta.Phys.Sin. 555611(in Chinese) [马松华、方建平 2006 55 5611]
[57] Fan E G 2000 Phys.Lett. A 277212
[58] [59] [60] Chen Y, Li B, Zhang H Q 2003Chin.Phys. 12 940
[61] Chen Y, Yan Z Y, Li B, Zhang H Q 2003Chin.Phys. 121
[62] [63] [64] Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 137
[65] [66] Li D S, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 143
[67] [68] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 39 647
[69] [70] L Z S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 405
[71] Bai C L 2003 Commun.Theor.Phys.(Beijing)40 147
[72] [73] Li D S, Zhang H Q 2004Chin.Phys. 13984
-
[1] Zhang L, Zhang L F, Li C Y2008Chin.Phys.B 17 403
[2] [3] [4] Wu H Y, Zhang L, Tan Y K, Zhou X T 2008Acta.Phys.Sin. 57 3312(in Chinese) [吴海燕、张 亮、谭言科、周小滔 2008 57 3312]
[5] [6] Gao L, Xu W, Tang Y N, Shen J W 2007Acta.Phys.Sin. 561860(in Chinese)[高 亮、徐 伟、唐亚宁、申建伟 2007 56 1860]
[7] Xu G Q, Li Z B 2003Acta.Phys.Sin. 521848(in Chinese)[徐桂琼、李志斌 2003 52 1848]
[8] [9] [10] Wang M L 1995 Phys.Lett. A 199 169
[11] [12] Wu Y Q 2008 Acta.Phys.Sin. 57 5390(in Chinese)[吴勇旗 2008 57 5390]
[13] [14] He F, Guo Q B, Liu L 2007 Acta.Phys.Sin. 56 4326(in Chinese)[贺 锋、郭启波、 刘 辽 2007 56 4326]
[15] Zhang S Q, Li Z B 2003Acta.Phys.Sin. 52 1067(in Chinese)[张善卿、李志斌 2003 52 1067]
[16] [17] Wang Z, Li D S,Lu H F,Zhang H Q2005 Chin.Phys. 14 2158
[18] [19] Parkes E J, Duffy B R 1996Comput.Phys.Commun. 98288
[20] [21] Sirendaoreji, Sun J 2003Phys. Lett.A309387
[22] [23] Fu Z T, Liu S D, Liu S K 2003Commun.Theor.Phys.(Beijing,China) 39 531
[24] [25] Zhao X Q, Zhi H Y, Zhang H Q 2006Chin.Phys. 15 2202
[26] [27] [28] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin.Phys. 12 825
[29] [30] Lu B, Zhang H Q 2008Chin.Phys.B 17 3974
[31] [32] Li H M 2005Chin.Phys. 14251
[33] [34] Zhu J M, Zheng C L, Ma Z Y 2004Chin.Phys. 132008
[35] Taogetusang, Sirendaoerji 2006 Chin.Phys. 15 2809
[36] [37] Pan J T, Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese)[潘军廷、龚伦训 2007 56 5585]
[38] [39] Sirendaoerji2003 J.Modern.Phys. C 14 1075
[40] [41] Ma S H, Wu X H, Fang J P, Zheng C L 2008 Acta.Phys.Sin. 57 11(in Chinese) [马松华、 吴小红、 方建平、 郑春龙 2008 57 11]
[42] [43] [44] Ma S H,Fang J P,Zheng C L2008 Chin.Phys.B 172767
[45] [46] Chen Y, Li B 2004 Commun.Theor.Phys.(Beijing, China) 41 1
[47] [48] Liu C S 2005 Acta.Phys.Sin. 544506(in Chinese)[刘成仕 2005 544506]
[49] Li D S, Zhang H Q 2003 Acta.Phys.Sin. 521569(in Chinese)[李德生、张鸿庆 2003 521569]
[50] [51] [52] Lu D C, Hong B J, Tian L X2006 Acta.Phys.Sin. 555617(in Chinese)[卢殿臣、烘宝剑、田立新 2006 555617]
[53] [54] Mao J J, Yang J R2005Acta.Phys.Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[55] [56] Ma S H, Fang J P 2006Acta.Phys.Sin. 555611(in Chinese) [马松华、方建平 2006 55 5611]
[57] Fan E G 2000 Phys.Lett. A 277212
[58] [59] [60] Chen Y, Li B, Zhang H Q 2003Chin.Phys. 12 940
[61] Chen Y, Yan Z Y, Li B, Zhang H Q 2003Chin.Phys. 121
[62] [63] [64] Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 137
[65] [66] Li D S, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 40 143
[67] [68] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys. (Beijing) 39 647
[69] [70] L Z S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 405
[71] Bai C L 2003 Commun.Theor.Phys.(Beijing)40 147
[72] [73] Li D S, Zhang H Q 2004Chin.Phys. 13984
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