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To construct the infinite sequence soliton-like exact solutions of nonlinear evolution equations and develop the characteristics of constructivity and mechanization of the first kind of elliptic equation, new type of solutions and the corresponding Bcklund transformation of the equation are presented. Based on this, infinite sequence soliton-like exact solutions of Nizhnik-Novikov-Vesselov equation are obtained with the help of symbolic computation system Mathematica, which includes infinite sequence smooth soliton-like solutions, infinite sequence peak soliton-like solutions and infinite sequence compact soliton-like solutions.
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Keywords:
- the first kind of elliptic equation /
- Bcklund transformation /
- Nizhnik-Novikov-Vesselov equation /
- infinite sequence exact solution
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[3] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 40 137
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[5] Zhang L, Zhang L F, Li C Y 2008 Chin. Phys. B 17 403
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[11] Taogetusang, Sirendaoerji 2010 Acta. Phys. Sin. 59 4413 (in Chinese) [套格图桑, 斯仁道尔吉 2010 59 4413]
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[13] Xie F D, Yuan Z T 2005 Commun. Theor. Phys. 43 39
[14] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 39 647
[15] Xie F D, Gao X S 2004 Commun. Theor. Phys. 41 353
[16] Chen Y, Li B 2004 Commun. Theor. Phys. 41 1
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[18] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
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[20] Lü Z S, Zhang H Q 2003 Commun. Theor. Phys. 39 405
[21] Xie F D, Chen J, Lü Z S 2005 Commun. Theor. Phys. 43 585
[22] 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 56 4319]
[23] 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]
[24] Pan Z H, Ma S H, Fang J P 2010 Chin. Phys. B 19 100301
[25] Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[26] Xu G Q, Li Z B 2003 Commun. Theor. Phys. 39 39
[27] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
[28] Taogetusang, Sirendaoerji 2011 Journal of Inner Mongolia University 42 344 (in Chinese) [套格图桑, 斯仁道尔吉 2011 内蒙古大学学报 42 344]
[29] Jiao X Y, Wang J H, Zhang H Q 2005 Commun. Theor. Phys. 44 407
[30] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[31] Rosenau P, Hyman J 1993 Phys. Rev. Lett. 70 564
[32] Dullin H R, Gottwald G A, Holm D D 2002 Phys. Rev. Lett. 87 4501
[33] Guo B L, Liu Z R 2003 Sci. China A 33 325 (in Chinese) [郭柏灵, 刘正荣 2003 中国科学 A 33 325]
[34] Yin J L, Tian L X 2009 Acta Phys. Sin. 58 3632 (in Chinese) [殷久利, 田立新 2009 58 3632]
[35] Yu L Q, Tian L X 2006 Math. Practice Theory 36 261 (in Chinese) [余丽琴, 田立新 2006 数学的实践与认识 36 261]
[36] Yu L Q, Tian L X 2005 Pure Appl. Math. 21 310 (in Chinese) [余丽琴, 田立新 2005 纯粹数学与应用数学 21 310]
[37] Yan Z Y 2002 Chaos Soliton. Fract. 14 1151
[38] Yin J L, Tian L X 2007 Acta Math. Phys. 27 27 (in Chinese) [殷久利, 田立新 2007 数学 27 27]
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[1] Fan E G 2000 Phys. Lett. A 277 212
[2] Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[3] Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 40 137
[4] Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[5] Zhang L, Zhang L F, Li C Y 2008 Chin. Phys. B 17 403
[6] Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin. Phys. 15 2202
[7] Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[8] Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303(1)
[9] 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]
[10] Taogetusang, Sirendaoerji 2010 Acta Phys. Sin. 59 5194 (in Chinese) [套格图桑, 斯仁道尔吉 2010 59 5194]
[11] Taogetusang, Sirendaoerji 2010 Acta. Phys. Sin. 59 4413 (in Chinese) [套格图桑, 斯仁道尔吉 2010 59 4413]
[12] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
[13] Xie F D, Yuan Z T 2005 Commun. Theor. Phys. 43 39
[14] Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 39 647
[15] Xie F D, Gao X S 2004 Commun. Theor. Phys. 41 353
[16] Chen Y, Li B 2004 Commun. Theor. Phys. 41 1
[17] Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[18] Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[19] Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[20] Lü Z S, Zhang H Q 2003 Commun. Theor. Phys. 39 405
[21] Xie F D, Chen J, Lü Z S 2005 Commun. Theor. Phys. 43 585
[22] 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 56 4319]
[23] 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]
[24] Pan Z H, Ma S H, Fang J P 2010 Chin. Phys. B 19 100301
[25] Qiang J Y, Ma S H, Fang J P 2010 Chin. Phys. B 19 090305
[26] Xu G Q, Li Z B 2003 Commun. Theor. Phys. 39 39
[27] Chen H T, Zhang H Q 2004 Commun. Theor. Phys. 42 497
[28] Taogetusang, Sirendaoerji 2011 Journal of Inner Mongolia University 42 344 (in Chinese) [套格图桑, 斯仁道尔吉 2011 内蒙古大学学报 42 344]
[29] Jiao X Y, Wang J H, Zhang H Q 2005 Commun. Theor. Phys. 44 407
[30] Camassa R, Holm D D 1993 Phys. Rev. Lett. 71 1661
[31] Rosenau P, Hyman J 1993 Phys. Rev. Lett. 70 564
[32] Dullin H R, Gottwald G A, Holm D D 2002 Phys. Rev. Lett. 87 4501
[33] Guo B L, Liu Z R 2003 Sci. China A 33 325 (in Chinese) [郭柏灵, 刘正荣 2003 中国科学 A 33 325]
[34] Yin J L, Tian L X 2009 Acta Phys. Sin. 58 3632 (in Chinese) [殷久利, 田立新 2009 58 3632]
[35] Yu L Q, Tian L X 2006 Math. Practice Theory 36 261 (in Chinese) [余丽琴, 田立新 2006 数学的实践与认识 36 261]
[36] Yu L Q, Tian L X 2005 Pure Appl. Math. 21 310 (in Chinese) [余丽琴, 田立新 2005 纯粹数学与应用数学 21 310]
[37] Yan Z Y 2002 Chaos Soliton. Fract. 14 1151
[38] Yin J L, Tian L X 2007 Acta Math. Phys. 27 27 (in Chinese) [殷久利, 田立新 2007 数学 27 27]
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