Several auxiliary equations and infinite sequence exactsolutions to nonlinear evolution equations

Taogetusang

doi:10.7498/aps.60.050201

Abstract

To seek infinite sequence exact solutions of nonlinear evolution equations, the Böcklund transformation of the solutions to some auxiliary equations and the formula of nonlinear superimposition of solutions are presented for constructing infinite sequence exact solutions to nonlinear evolution equations, which include infinite sequence Jacobi elliptic function solutions, infinite sequence hyperbolic function solutions and infinite sequence trigonomical function solutions. The method is of significance to the search into infinite sequence exact solutions of other nonlinear evolution equations.

Keywords:

Authors and contacts

Taogetusang

1.
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

References

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[2]	Gardner C S, Greene J M, Kruskal M D, Miura R M 1967 Phys.Rev.Lett. 19 1095
[3]	Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Comn.Pure.Appi.Math. 27 97
[4]	Miura R M 1976 SIAM.Rev. 18 412
[5]	Wang M L 1995 Phys.Lett.A 199 169
[6]	Parkes E J, Duffy B R 1996 Comput.Phys.Commun. 98 288
[7]	Fan E G 2000 Phys.Lett.A 277 212
[8]	Chen Y, Li B, Zhang H Q 2003 Chin.Phys. 12 940
[9]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin.Phys. 12 1
[10]	Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 40 137
[11]	Li D S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 40 143
[12]	Li D S, Zhang H Q 2004 Chin.Phys. 13 984
[13]	Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[14]	Chen H T, Zhang H Q 2004 Commun.Theor.Phys.(Beijing) 42 497
[15]	Xie F D, Chen J, Lü Z S 2005 Commun.Theor.Phys.(Beijing) 43 585
[16]	Xie F D,Yuan Z T 2005 Commun.Theor.Phys.(Beijing) 43 39
[17]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 647
[18]	Lü Z S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 405
[19]	Xie F D, Gao X S 2004 Commun.Theor.Phys.(Beijing) 41 353
[20]	Chen Y, Li B 2004 Commun.Theor.Phys.(Beijing) 41 1
[21]	Ma S H, Fang J P, Zhu H P 2007 Acta.Phys.Sin. 56 4319(in Chinese)[马松华、方建平、朱海平 2007 物理学报 56 4319]
[22]	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 物理学报 57 11]
[23]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 1569(in Chinese) [李德生、张鸿庆 2003 物理学报 52 1569]
[24]	Zeng X, Zhang H Q 2005 Acta.Phys.Sin. 54 504(in Chinese)[曾昕、张鸿庆 2005 物理学报 54 504]
[25]	Zhi H Y, Wang Q, Zhang H Q 2005 Acta.Phys.Sin. 54 1002(in Chinese)[智红燕、王琪、张鸿庆 2005 物理学报 54 1002]
[26]	Pan J T, Gong L X 2008 Chin.Phys. B 17 399
[27]	Jiao X Y, Wang J H,Zhang H Q 2005 Commun.Theor.Phys.(Beijing)44 407
[28]	Liu Y P, Li Z B 2003 Chin.Phys.Lett. 20 317
[29]	Xu G Q, Li Z B 2003 Commun.Theor.Phys.(Beijing) 39 39
[30]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 6214]
[31]	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]
[32]	Li Z L 2009 Chin.Phys.B 18 4074
[33]	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 55 5617]
[34]	Huang D J, Zhang H Q 2004 Acta.Phys.Sin. 53 2434(in Chinese)[黄定江、张鸿庆 2004 物理学报 53 2434]
[35]	Zhang S Q, Li Z B 2002 Acta.Phys.Sin. 51 2197(in Chinese)[张善卿、李志斌 2002 物理学报 51 2197]
[36]	Zhao X Q, Tang D B,Wang L M,Zhang Y M 2003 Acta.Phys.Sin. 52 1827(in Chinese)[赵熙强、唐登斌、王利民、张耀明 2002 物理学报 51 2197]
[37]	Wang Z,Li D S, Lu H F,Zhang H Q 2005 Chin.Phys. 14 2158
[38]	Li D S, Zhang H Q 2006 Acta.Phys.Sin. 55 1565(in Chinese)[李德生、张鸿庆 2006 物理学报 55 1565]
[39]	Yong X L, Zhang H Q 2005 Acta.Phys.Sin. 54 2514(in Chinese)[雍雪林、张鸿庆 2005 物理学报 54 2514]
[40]	Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[41]	Lu B, Zhang H Q 2008 Chin.Phys.B 17 3974
[42]	Wang Z, Zhang H Q 2006 Chin.Phys. 15 2210
[43]	Zhang J L,Ren D F,Wang M L,Wang Y M, Fang Z D 2003 Chin.Phys. 12 825
[44]	Zhang L,Zhang L F,Li C Y 2008 Chin.Phys.B 17 403
[45]	Zhao X Q,Zhi H Y,Zhang H Q 2006 Chin.Phys. 15 2202
[46]	Li J B 2007 Scie.Chin.Ser.Math.A 50 153
[47]	Li H M 2003 Commun.Theor.Phys.(Beijing) 39 395
[48]	Li H M 2005 Chin.Phys. 14 251
[49]	Li H M 2002 Chin.Phys. 11 1111
[50]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 2809
[51]	Liu C S 2005 Chin.Phys. 14 1710
[52]	Zhu J M,Zheng C L,Ma Z Y 2004 Chin.Phys. 13 2008
[53]	Fu Z T,Liu S D,Liu S K 2003 Commun.Theor.Phys.(Beijing) 39 531
[54]	Fu Z T,Liu S K,Liu S D 2004 Commun.Theor.Phys.(Beijing) 42 343
[55]	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]
[56]	Liu C S,Du X H 2005 Acta.Phys.Sin. 54 1039(in Chinese)[刘成仕、杜兴华 2005 物理学报 54 1039]
[57]	Pan J T,Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese) [潘军廷、龚伦训 2007 物理学报 56 5585]
[58]	Taogetusang, Sirendaoerji 2008 Acta.Phys.Sin. 57 1295(in Chinese) [套格图桑、斯仁道尔吉 2008 物理学报 57 1295]
[59]	Sirendaoerji,Sun J 2003 Phys.Lett.A 309 387
[60]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 3246(in Chinese) [套格图桑、斯仁道尔吉 2006 物理学报 55 3246]
[61]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 1143
[62]	Taogetusang, Sirendaoerji 2007 Acta.Phys.Sin. 56 627(in Chinese) [套格图桑、斯仁道尔吉 2007 物理学报 56 627]
[63]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 13(in Chinese) [套格图桑、斯仁道尔吉 2006 物理学报 55 13]
[64]	Mao J J, Yang J R 2005 Acta.Phys.Sin. 54 4999(in Chinese) [毛杰健、杨建荣 2005 物理学报 54 4999]
[65]	Fu Z T,Liu S K,Liu S D 2003 Commun.Theor.Phys.(Beijing) 39 27
[66]	Yu J,Ke Y Q,Zhang W J 2004 Commun.Theor.Phys.(Beijing) 40 493
[67]	Sirendaoerji,Sun J 2002 Phys.Lett.A 298 133
[68]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 2373(in Chinese)[李德生、张鸿庆 2006 物理学报 52 2373]
[69]	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 物理学报 53 343]
[70]	Zhao C H, Sheng Z M 2004 Acta.Phys.Sin. 53 1629(in Chinese)[赵长海、盛正卯 2004 物理学报 53 1629]
[71]	He F,Guo Q B, Liu L 2007 Acta.Phys.Sin. 56 4326(in Chinese)[贺锋、郭启波、刘辽 2007 物理学报 56 4326]
[72]	Taogetusang, Sirendaoerji,Wang Q P 2009 Acta Sci.J.Nat.Univ.NeiMongol 38 387(in Chinese) [套格图桑、斯仁道尔吉、王庆鹏 2009 内蒙古师范大学学报 38 387]
[73]	Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 4413(in Chinese) [套格图桑、斯仁道尔吉 2010 物理学报 59 4413]
[74]	Narenmandula 2002 Acta.Phys.Sin. 51 1671(in Chinese)[那仁满都拉 2002 物理学报 51 1671]
[75]	Narenmandula,Wang K X 2003 Acta.Phys.Sin. 52 1565(in Chinese)[那仁满都拉、王克协 2003 物理学报 52 1565]

Cited By

[1]	Zabusky N, Kruskal M D 1965 Phys.Rev.Lett. 15 240
[2]	Gardner C S, Greene J M, Kruskal M D, Miura R M 1967 Phys.Rev.Lett. 19 1095
[3]	Gardner C S, Greene J M, Kruskal M D, Miura R M 1974 Comn.Pure.Appi.Math. 27 97
[4]	Miura R M 1976 SIAM.Rev. 18 412
[5]	Wang M L 1995 Phys.Lett.A 199 169
[6]	Parkes E J, Duffy B R 1996 Comput.Phys.Commun. 98 288
[7]	Fan E G 2000 Phys.Lett.A 277 212
[8]	Chen Y, Li B, Zhang H Q 2003 Chin.Phys. 12 940
[9]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin.Phys. 12 1
[10]	Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 40 137
[11]	Li D S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 40 143
[12]	Li D S, Zhang H Q 2004 Chin.Phys. 13 984
[13]	Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[14]	Chen H T, Zhang H Q 2004 Commun.Theor.Phys.(Beijing) 42 497
[15]	Xie F D, Chen J, Lü Z S 2005 Commun.Theor.Phys.(Beijing) 43 585
[16]	Xie F D,Yuan Z T 2005 Commun.Theor.Phys.(Beijing) 43 39
[17]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 647
[18]	Lü Z S, Zhang H Q 2003 Commun.Theor.Phys.(Beijing) 39 405
[19]	Xie F D, Gao X S 2004 Commun.Theor.Phys.(Beijing) 41 353
[20]	Chen Y, Li B 2004 Commun.Theor.Phys.(Beijing) 41 1
[21]	Ma S H, Fang J P, Zhu H P 2007 Acta.Phys.Sin. 56 4319(in Chinese)[马松华、方建平、朱海平 2007 物理学报 56 4319]
[22]	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 物理学报 57 11]
[23]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 1569(in Chinese) [李德生、张鸿庆 2003 物理学报 52 1569]
[24]	Zeng X, Zhang H Q 2005 Acta.Phys.Sin. 54 504(in Chinese)[曾昕、张鸿庆 2005 物理学报 54 504]
[25]	Zhi H Y, Wang Q, Zhang H Q 2005 Acta.Phys.Sin. 54 1002(in Chinese)[智红燕、王琪、张鸿庆 2005 物理学报 54 1002]
[26]	Pan J T, Gong L X 2008 Chin.Phys. B 17 399
[27]	Jiao X Y, Wang J H,Zhang H Q 2005 Commun.Theor.Phys.(Beijing)44 407
[28]	Liu Y P, Li Z B 2003 Chin.Phys.Lett. 20 317
[29]	Xu G Q, Li Z B 2003 Commun.Theor.Phys.(Beijing) 39 39
[30]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 6214(in Chinese)[套格图桑、斯仁道尔吉 2006 物理学报 55 6214]
[31]	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]
[32]	Li Z L 2009 Chin.Phys.B 18 4074
[33]	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 55 5617]
[34]	Huang D J, Zhang H Q 2004 Acta.Phys.Sin. 53 2434(in Chinese)[黄定江、张鸿庆 2004 物理学报 53 2434]
[35]	Zhang S Q, Li Z B 2002 Acta.Phys.Sin. 51 2197(in Chinese)[张善卿、李志斌 2002 物理学报 51 2197]
[36]	Zhao X Q, Tang D B,Wang L M,Zhang Y M 2003 Acta.Phys.Sin. 52 1827(in Chinese)[赵熙强、唐登斌、王利民、张耀明 2002 物理学报 51 2197]
[37]	Wang Z,Li D S, Lu H F,Zhang H Q 2005 Chin.Phys. 14 2158
[38]	Li D S, Zhang H Q 2006 Acta.Phys.Sin. 55 1565(in Chinese)[李德生、张鸿庆 2006 物理学报 55 1565]
[39]	Yong X L, Zhang H Q 2005 Acta.Phys.Sin. 54 2514(in Chinese)[雍雪林、张鸿庆 2005 物理学报 54 2514]
[40]	Li D S, Zhang H Q 2004 Chin.Phys. 13 1377
[41]	Lu B, Zhang H Q 2008 Chin.Phys.B 17 3974
[42]	Wang Z, Zhang H Q 2006 Chin.Phys. 15 2210
[43]	Zhang J L,Ren D F,Wang M L,Wang Y M, Fang Z D 2003 Chin.Phys. 12 825
[44]	Zhang L,Zhang L F,Li C Y 2008 Chin.Phys.B 17 403
[45]	Zhao X Q,Zhi H Y,Zhang H Q 2006 Chin.Phys. 15 2202
[46]	Li J B 2007 Scie.Chin.Ser.Math.A 50 153
[47]	Li H M 2003 Commun.Theor.Phys.(Beijing) 39 395
[48]	Li H M 2005 Chin.Phys. 14 251
[49]	Li H M 2002 Chin.Phys. 11 1111
[50]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 2809
[51]	Liu C S 2005 Chin.Phys. 14 1710
[52]	Zhu J M,Zheng C L,Ma Z Y 2004 Chin.Phys. 13 2008
[53]	Fu Z T,Liu S D,Liu S K 2003 Commun.Theor.Phys.(Beijing) 39 531
[54]	Fu Z T,Liu S K,Liu S D 2004 Commun.Theor.Phys.(Beijing) 42 343
[55]	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]
[56]	Liu C S,Du X H 2005 Acta.Phys.Sin. 54 1039(in Chinese)[刘成仕、杜兴华 2005 物理学报 54 1039]
[57]	Pan J T,Gong L X 2007 Acta.Phys.Sin. 56 5585(in Chinese) [潘军廷、龚伦训 2007 物理学报 56 5585]
[58]	Taogetusang, Sirendaoerji 2008 Acta.Phys.Sin. 57 1295(in Chinese) [套格图桑、斯仁道尔吉 2008 物理学报 57 1295]
[59]	Sirendaoerji,Sun J 2003 Phys.Lett.A 309 387
[60]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 3246(in Chinese) [套格图桑、斯仁道尔吉 2006 物理学报 55 3246]
[61]	Taogetusang,Sirendaoerji 2006 Chin.Phys. 15 1143
[62]	Taogetusang, Sirendaoerji 2007 Acta.Phys.Sin. 56 627(in Chinese) [套格图桑、斯仁道尔吉 2007 物理学报 56 627]
[63]	Taogetusang, Sirendaoerji 2006 Acta.Phys.Sin. 55 13(in Chinese) [套格图桑、斯仁道尔吉 2006 物理学报 55 13]
[64]	Mao J J, Yang J R 2005 Acta.Phys.Sin. 54 4999(in Chinese) [毛杰健、杨建荣 2005 物理学报 54 4999]
[65]	Fu Z T,Liu S K,Liu S D 2003 Commun.Theor.Phys.(Beijing) 39 27
[66]	Yu J,Ke Y Q,Zhang W J 2004 Commun.Theor.Phys.(Beijing) 40 493
[67]	Sirendaoerji,Sun J 2002 Phys.Lett.A 298 133
[68]	Li D S, Zhang H Q 2003 Acta.Phys.Sin. 52 2373(in Chinese)[李德生、张鸿庆 2006 物理学报 52 2373]
[69]	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 物理学报 53 343]
[70]	Zhao C H, Sheng Z M 2004 Acta.Phys.Sin. 53 1629(in Chinese)[赵长海、盛正卯 2004 物理学报 53 1629]
[71]	He F,Guo Q B, Liu L 2007 Acta.Phys.Sin. 56 4326(in Chinese)[贺锋、郭启波、刘辽 2007 物理学报 56 4326]
[72]	Taogetusang, Sirendaoerji,Wang Q P 2009 Acta Sci.J.Nat.Univ.NeiMongol 38 387(in Chinese) [套格图桑、斯仁道尔吉、王庆鹏 2009 内蒙古师范大学学报 38 387]
[73]	Taogetusang, Sirendaoerji 2010 Acta.Phys.Sin. 59 4413(in Chinese) [套格图桑、斯仁道尔吉 2010 物理学报 59 4413]
[74]	Narenmandula 2002 Acta.Phys.Sin. 51 1671(in Chinese)[那仁满都拉 2002 物理学报 51 1671]
[75]	Narenmandula,Wang K X 2003 Acta.Phys.Sin. 52 1565(in Chinese)[那仁满都拉、王克协 2003 物理学报 52 1565]

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Vol. 60, Issue 5 - 2011-03-05

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