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In order to obtain infinite sequence exact solutions to the sine-Gordon-type equations, the auxiliary equations of triangular function type and hyperbolic function type, Bäcklund transformation and nonlinear superposition formula of the solutions are presented. And the method is used to construct new infinite sequence exact solutions to the sine-Gordon equation, mKdV-sine-Gordon equation, (n+1)- dimensional double sine-Gordon equation and the sinh-Gordon equation with the help of symbolic computation system Mathematica, which include infinite sequence triangular function solutions, the infinite sequence hyperbolic function solutions, infinite sequence Jacobi elliptic function solutions and infinite sequence computation solutions.
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Keywords:
- sine-Gordon-type equations /
- solution of nonlinear superposition formula /
- auxiliary equation /
- infinite sequence exact solution
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[2] Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Comn. Pure. Appi. Math. 27 97
[3] Miura R M 1976 SIAM. Rev.18 412
[4] Wang M L 1995 Phys. Lett. A 199 169
[5] Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288
[6] Fan E G 2000 Phys. Lett. A 277 212
[7] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[8] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[9] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[10] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[11] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[12] Lü Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[13] Bai C L 2003 Commun. Theor. Phys. (Beijing) 40 147
[14] Li D S, Zhang H Q 2004 Chin.Phys.13 984
[15] Xie F D, Gao X S 2004 Commun. Theor. Phys. (Beijing) 41 353
[16] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[17] Xie F D, Chen J, Lü Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[18] Xie F D, Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
[19] Yong X L, Zhang H Q 2005 Acta.Phys.Sin.54 2514(in Chinese)[雍雪林、张鸿庆 2005 54 2514]
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[21] Wang Z, Zhang H Q 2006 Chin.Phys.15 2210
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[23] Xie Y X, Tang J S 2005 Chin.Phys. 14 1303
[24] Taogetusang, Sirendaoreji 2004 Acta Sci. J. Nat. Univ. NeiMongol 33 361(in Chinese)[套格图桑、斯仁道尔吉 2004 内蒙古师范大学学报 33 361]
[25] Taogetusang, Sirendaoerji 2007 Acta. Phys. Sin. 56 627(in Chinese) [套格图桑、斯仁道尔吉 2007 56 627]
[26] Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 13(in Chinese) [套格图桑、斯仁道尔吉 2006 55 13]
[27] Mao J J, Yang J R 2005 Acta.Phys.Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[28] Fu Z T, Liu S K, Liu S D 2003 Commun.Theor.Phys. (Beijing) 39 27
[29] Yu J, Ke Y Q, Zhang W J 2004 Commun.Theor.Phys. (Beijing) 40 493
[30] Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 2373(in Chinese)[李德生、张鸿庆 2006 52 2373]
[31] Fu Z T, Liu S K, Liu S D 2004 Acta.Phys.Sin.53 343(in Chinese)[付遵涛、刘式适、刘式达 2004 53 343]
[32] Zhao C H, Sheng Z M 2004 Acta.Phys.Sin.53 1629(in Chinese)[赵长海、盛正卯 2004 53 1629]
[33] 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]
[34] Guo F K 1983 Acta.Math.Sin.26 745(in Chinese)[郭福奎 1983 数学学报 26 745]
[35] Xu B Z, Fang X W 1992 Appl.Math.Mech.13 515(in Chinese)[徐宝智、方小卫 1992 应用数学和力学 13 515]
[36] Zhu Z W, Lu Y 2000 Chin. Quarterly J. Math. March 15 71
[37] Wang Y, Wang B, Qin M Z 2004 Science. China. Series. A Math. 47 18
[38] Sheng P X 2005 Acta.Math.Appl.Sin.28 453(in Chinese)[盛平兴 2005 应用数学学报 28 453]
[39] Li J B 2007 Science. China. A 50 153
[40] Wazwaz A M 2006 Phys.Lett. A 350 367
[41] Zhou J P, Yan Z L 2007 Chin.J.Quantum Electronics 24 535(in Chinese)[周建平、闫志莲 2007 量子电子学报 24 535]
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[1] Gardner C S, Greene J M, Kruskal M D, Miura R M 1967 Phys. Rev. Lett. 19 1095
[2] Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Comn. Pure. Appi. Math. 27 97
[3] Miura R M 1976 SIAM. Rev.18 412
[4] Wang M L 1995 Phys. Lett. A 199 169
[5] Parkes E J, Duffy B R 1996 Comput. Phys. Commun. 98 288
[6] Fan E G 2000 Phys. Lett. A 277 212
[7] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[8] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[9] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[10] Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[11] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[12] Lü Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[13] Bai C L 2003 Commun. Theor. Phys. (Beijing) 40 147
[14] Li D S, Zhang H Q 2004 Chin.Phys.13 984
[15] Xie F D, Gao X S 2004 Commun. Theor. Phys. (Beijing) 41 353
[16] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[17] Xie F D, Chen J, Lü Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[18] Xie F D, Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
[19] Yong X L, Zhang H Q 2005 Acta.Phys.Sin.54 2514(in Chinese)[雍雪林、张鸿庆 2005 54 2514]
[20] Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[21] Wang Z, Zhang H Q 2006 Chin.Phys.15 2210
[22] Sirendaoreji, Sun J 2002 Phys.Lett. A 298 133
[23] Xie Y X, Tang J S 2005 Chin.Phys. 14 1303
[24] Taogetusang, Sirendaoreji 2004 Acta Sci. J. Nat. Univ. NeiMongol 33 361(in Chinese)[套格图桑、斯仁道尔吉 2004 内蒙古师范大学学报 33 361]
[25] Taogetusang, Sirendaoerji 2007 Acta. Phys. Sin. 56 627(in Chinese) [套格图桑、斯仁道尔吉 2007 56 627]
[26] Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 13(in Chinese) [套格图桑、斯仁道尔吉 2006 55 13]
[27] Mao J J, Yang J R 2005 Acta.Phys.Sin. 54 4999(in Chinese)[毛杰健、杨建荣 2005 54 4999]
[28] Fu Z T, Liu S K, Liu S D 2003 Commun.Theor.Phys. (Beijing) 39 27
[29] Yu J, Ke Y Q, Zhang W J 2004 Commun.Theor.Phys. (Beijing) 40 493
[30] Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 2373(in Chinese)[李德生、张鸿庆 2006 52 2373]
[31] Fu Z T, Liu S K, Liu S D 2004 Acta.Phys.Sin.53 343(in Chinese)[付遵涛、刘式适、刘式达 2004 53 343]
[32] Zhao C H, Sheng Z M 2004 Acta.Phys.Sin.53 1629(in Chinese)[赵长海、盛正卯 2004 53 1629]
[33] 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]
[34] Guo F K 1983 Acta.Math.Sin.26 745(in Chinese)[郭福奎 1983 数学学报 26 745]
[35] Xu B Z, Fang X W 1992 Appl.Math.Mech.13 515(in Chinese)[徐宝智、方小卫 1992 应用数学和力学 13 515]
[36] Zhu Z W, Lu Y 2000 Chin. Quarterly J. Math. March 15 71
[37] Wang Y, Wang B, Qin M Z 2004 Science. China. Series. A Math. 47 18
[38] Sheng P X 2005 Acta.Math.Appl.Sin.28 453(in Chinese)[盛平兴 2005 应用数学学报 28 453]
[39] Li J B 2007 Science. China. A 50 153
[40] Wazwaz A M 2006 Phys.Lett. A 350 367
[41] Zhou J P, Yan Z L 2007 Chin.J.Quantum Electronics 24 535(in Chinese)[周建平、闫志莲 2007 量子电子学报 24 535]
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