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为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解.
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关键词:
- 第二种椭圆方程 /
- Riccati方程 /
- 非线性发展方程 /
- Riemann theta 函数无穷序列解
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:
- the second kind of elliptic equation /
- Riccati equation /
- nonlinear evolution equation /
- Riemann theta function infinite sequence solution
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[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
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[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
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[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
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[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
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[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
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[39] Sirendaoerji, Sun J 2003 Phys. Lett. A 309 387
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[43] 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]
[44] Fu Z T, Liu S K, Liu S D 2003 Commun. Theor. Phys. (Beijing) 39 27
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[48] Wang J M 2012 Acta Phys. Sin. 61 080201 (in Chinese) [王军民 2012 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 53 3265]
[57] Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 56 627]
[43] 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]
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 53 3265]
[57] Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. (Beijing) 55 949
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