Riemann theta function and other several kinds of new solutions of nonlinear evolution equations

Taogetusang; Bai Yu Mei

doi:10.7498/aps.62.100201

Abstract

Riemann theta function and other several kinds of new solutions to the second kind of elliptic equation are obtained to construct the infinite sequence complexiton solutions of nonlinear evolution equations. Based on this, applying Bcklund transformation and nonlinear superposition formula of the solutions to the second kind of elliptic equation and Riccati equation, mKdV equation is chosen as an example to seek infinite sequence new complexiton solutions with the help of symbolic computation system Mathematica, which are composed of Riemann theta function, Jacobi elliptic function, hyperbolic function, triangular function and rational function in several forms.

Keywords:

Authors and contacts

Taogetusang^1,2,
Bai Yu Mei¹

1.
The College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, China;
2.
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China
Funds: Project supported by the Natural Natural Science Foundation of China (Grant No. 10862003), the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZY12031) and the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant No. 2010MS0111).

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[44]	Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing) 39 27
[45]	Yu J, Ke Y Q, Zhang W J 2004 Commun. Theor. Phys. (Beijing) 40 493
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[47]	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]
[48]	Wang J M 2012 Acta Phys. Sin. 61 080201 (in Chinese) [王军民 2012 61 080201]
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[50]	Li D S, Zhang H Q 2006 Acta Phys. Sin. 55 1565 (in Chinese) [李德生, 张鸿庆 2006 55 1565]
[51]	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 57 3312]
[52]	Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 10 (in Chinese) [刘式适,付遵涛,刘式达,赵强 2002 51 10]
[53]	Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2069 (in Chinese) [刘式适,付遵涛,刘式达,赵强 2001 50 2069]
[54]	Liu S K, Fu Z T, Wang Z G, Liu S D 2003 Acta Phys. Sin. 52 1838 (in Chinese) [刘式适, 付遵涛,王彰贵,刘式达 2003 52 1838]
[55]	Liu S K, Chen H, Fu Z T, Liu S D 2003 Acta Phys. Sin. 52 1843 (in Chinese) [刘式适,陈华,付遵涛,刘式达 2003 52 1843]
[56]	Shi Y R, Guo P, L K P, Duan W S 2004 Acta Phys. Sin. 53 3265 (in Chinese) [石玉仁, 郭鹏,吕克璞,段文山 2004 53 3265]
[57]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949

Cited By

[1]	Fan E G 2000 Phys. Lett. A 277 212
[2]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[3]	Chen Y, Yan Z Y, Li B, Zhang H Q 2003 Chin. Phys. 12 1
[4]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 137
[5]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 40 143
[6]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[7]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[8]	Chen H T, Zhang H Q 2004 Commun. Theor. Phys. (Beijing) 42 497
[9]	Xie F D, Chen J, L Z S 2005 Commun. Theor. Phys. (Beijing) 43 585
[10]	Xie F D, Yuan Z T 2005 Commun. Theor. Phys. (Beijing) 43 39
[11]	Zhen X D, Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 647
[12]	L Z S, Zhang H Q 2003 Commun. Theor. Phys. (Beijing) 39 405
[13]	Xie F D, Gao X S 2004 Commun. Theor. Phys. (Beijing) 41 353
[14]	Chen Y, Li B 2004 Commun. Theor. Phys. (Beijing) 41 1
[15]	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]
[16]	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]
[17]	Pan J T, Gong L X 2008 Chin. Phys. B 17 399
[18]	Jiao X Y, Wang J H, Zhang H Q 2005 Commun. Theor. Phys. (Beijing) 44 407
[19]	Liu Y P, Li Z B 2003 Chin. Phys. Lett. 20 317
[20]	Xu G Q, Li Z B 2003 Commun. Theor. Phys. (Beijing) 39 39
[21]	Li Z L 2009 Chin. Phys. B 18 4074
[22]	Wang Z, Li D S, Lu H F, Zhang H Q 2005 Chin. Phys. 14 2158
[23]	Li D S, Zhang H Q 2004 Chin. Phys. 13 1377
[24]	Lu B, Zhang H Q 2008 Chin. Phys. B 17 3974
[25]	Wang Z, Zhang H Q 2006 Chin. Phys. 15 2210
[26]	Zhang J L, Ren D F, Wang M L, Wang Y M, Fang Z D 2003 Chin. Phys. 12 825
[27]	Zhang L, Zhang L F, Li C Y 2008 Chin. Phys. B 17 403
[28]	Zhao X Q, Zhi H Y, Zhang H Q 2006 Chin. Phys. 15 2202
[29]	Li J B 2007 Sci. Chin. Math. A 50 153
[30]	Li H M 2003 Commun. Theor. Phys. (Beijing) 39 395
[31]	Li H M 2005 Chin. Phys. 14 251
[32]	Li H M 2002 Chin. Phys. 11 1111
[33]	Taogetusang, Sirendaoerji 2006 Chin. Phys. 15 2809
[34]	Liu C S 2005 Chin. Phys. 14 1710
[35]	Zhu J M, Zheng C L, Ma Z Y 2004 Chin. Phys. 13 2008
[36]	Fu Z T, Liu S D, Liu S K 2003 Commun. Theor. Phys. (Beijing) 39 531
[37]	Fu Z T, Liu S K, Liu S D 2004 Commun. Theor. Phys. (Beijing) 42 343
[38]	Taogetusang, Sirendaoerji 2008 Acta Phys. Sin. 57 1295 (in Chinese) [套格图桑,斯仁道尔吉 2008 57 1295]
[39]	Sirendaoerji, Sun J 2003 Phys. Lett. A 309 387
[40]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 3246 (in Chinese) [套格图桑,斯仁道尔吉 2006 55 3246]
[41]	Taogetusang, Sirendaoerji 2006 Chin. Phys. 15 1143
[42]	Taogetusang, Sirendaoerji 2007 Acta Phys. Sin. 56 627 (in Chinese) [套格图桑,斯仁道尔吉 2007 56 627]
[43]	Taogetusang, Sirendaoerji 2006 Acta Phys. Sin. 55 13 (in Chinese) [套格图桑,斯仁道尔吉 2006 55 13]
[44]	Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing) 39 27
[45]	Yu J, Ke Y Q, Zhang W J 2004 Commun. Theor. Phys. (Beijing) 40 493
[46]	Sirendaoerji, Sun J 2002 Phys. Lett. A 298 133
[47]	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]
[48]	Wang J M 2012 Acta Phys. Sin. 61 080201 (in Chinese) [王军民 2012 61 080201]
[49]	Lawden D F 1989 Elliptic Functions and Applications (Berlin: Springer-Verlag) p496
[50]	Li D S, Zhang H Q 2006 Acta Phys. Sin. 55 1565 (in Chinese) [李德生, 张鸿庆 2006 55 1565]
[51]	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 57 3312]
[52]	Liu S K, Fu Z T, Liu S D, Zhao Q 2002 Acta Phys. Sin. 51 10 (in Chinese) [刘式适,付遵涛,刘式达,赵强 2002 51 10]
[53]	Liu S K, Fu Z T, Liu S D, Zhao Q 2001 Acta Phys. Sin. 50 2069 (in Chinese) [刘式适,付遵涛,刘式达,赵强 2001 50 2069]
[54]	Liu S K, Fu Z T, Wang Z G, Liu S D 2003 Acta Phys. Sin. 52 1838 (in Chinese) [刘式适, 付遵涛,王彰贵,刘式达 2003 52 1838]
[55]	Liu S K, Chen H, Fu Z T, Liu S D 2003 Acta Phys. Sin. 52 1843 (in Chinese) [刘式适,陈华,付遵涛,刘式达 2003 52 1843]
[56]	Shi Y R, Guo P, L K P, Duan W S 2004 Acta Phys. Sin. 53 3265 (in Chinese) [石玉仁, 郭鹏,吕克璞,段文山 2004 53 3265]
[57]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949

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Vol. 62, Issue 10 - 2013-05-20

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