搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

非线性发展方程的Riemann theta 函数等几种新解

套格图桑 白玉梅

引用本文:
Citation:

非线性发展方程的Riemann theta 函数等几种新解

套格图桑, 白玉梅

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

Taogetusang, Bai Yu Mei
PDF
导出引用
  • 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.
    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.
    • 基金项目: 国家自然科学基金(批准号: 10862003)、内蒙古自治区高等学校科学研究基金 (批准号: NJZY12031)和 内蒙古自治区自然科学基金(批准号: 2010MS0111)资助的课题.
    • 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).
    [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

  • [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

  • [1] 套格图桑, 伊丽娜. 一类非线性发展方程的复合型双孤子新解. 物理学报, 2015, 64(2): 020201. doi: 10.7498/aps.64.020201
    [2] 套格图桑. 构造非线性发展方程的无穷序列复合型类孤子新解. 物理学报, 2013, 62(7): 070202. doi: 10.7498/aps.62.070202
    [3] 成建军, 张鸿庆. 非线性发展方程的Wronskian解及Young图证明. 物理学报, 2013, 62(20): 200504. doi: 10.7498/aps.62.200504
    [4] 套格图桑, 白玉梅. 构造非线性发展方程无穷序列类孤子精确解的一种方法. 物理学报, 2012, 61(13): 130202. doi: 10.7498/aps.61.130202
    [5] 套格图桑. Degasperis-Procesi 方程的无穷序列尖峰孤立波解. 物理学报, 2011, 60(7): 070204. doi: 10.7498/aps.60.070204
    [6] 套格图桑. 几种辅助方程与非线性发展方程的无穷序列精确解. 物理学报, 2011, 60(5): 050201. doi: 10.7498/aps.60.050201
    [7] 套格图桑. 构造非线性发展方程无穷序列复合型精确解的一种方法. 物理学报, 2011, 60(1): 010202. doi: 10.7498/aps.60.010202
    [8] 套格图桑, 那仁满都拉. 第二种椭圆方程构造变系数非线性发展方程的无穷序列新精确解. 物理学报, 2011, 60(9): 090201. doi: 10.7498/aps.60.090201
    [9] 套格图桑, 斯仁道尔吉. 用Riccati方程构造非线性差分微分方程新的精确解. 物理学报, 2009, 58(9): 5894-5902. doi: 10.7498/aps.58.5894
    [10] 莫嘉琪, 张伟江, 何 铭. 强非线性发展方程孤波近似解. 物理学报, 2007, 56(4): 1843-1846. doi: 10.7498/aps.56.1843
    [11] 吴国将, 张 苗, 史良马, 张文亮, 韩家骅. 扩展的Jacobi椭圆函数展开法和Zakharov方程组的新的精确周期解. 物理学报, 2007, 56(9): 5054-5059. doi: 10.7498/aps.56.5054
    [12] 吴国将, 韩家骅, 史良马, 张 苗. 一般变换下双Jacobi椭圆函数展开法及应用. 物理学报, 2006, 55(8): 3858-3863. doi: 10.7498/aps.55.3858
    [13] 套格图桑, 斯仁道尔吉. 构造非线性发展方程精确解的一种方法. 物理学报, 2006, 55(12): 6214-6221. doi: 10.7498/aps.55.6214
    [14] 刘成仕. 试探方程法及其在非线性发展方程中的应用. 物理学报, 2005, 54(6): 2505-2509. doi: 10.7498/aps.54.2505
    [15] 韩兆秀. 非线性Klein-Gordon方程新的精确解. 物理学报, 2005, 54(4): 1481-1484. doi: 10.7498/aps.54.1481
    [16] 吕大昭. 非线性发展方程的丰富的Jacobi椭圆函数解. 物理学报, 2005, 54(10): 4501-4505. doi: 10.7498/aps.54.4501
    [17] 刘官厅, 范天佑. 一般变换下的Jacobi椭圆函数展开法及应用. 物理学报, 2004, 53(3): 676-679. doi: 10.7498/aps.53.676
    [18] 张善卿, 李志斌. Jacobi 椭圆函数展开法的新应用. 物理学报, 2003, 52(5): 1066-1070. doi: 10.7498/aps.52.1066
    [19] 徐桂琼, 李志斌. 构造非线性发展方程孤波解的混合指数方法. 物理学报, 2002, 51(5): 946-950. doi: 10.7498/aps.51.946
    [20] 刘春平. 一类非线性耦合方程的孤子解. 物理学报, 2000, 49(10): 1904-1908. doi: 10.7498/aps.49.1904
计量
  • 文章访问数:  4036
  • PDF下载量:  938
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-08-16
  • 修回日期:  2013-01-25
  • 刊出日期:  2013-05-05

非线性发展方程的Riemann theta 函数等几种新解

  • 1. 内蒙古民族大学数学学院, 通辽 028043;
  • 2. 内蒙古师范大学数学科学学院, 呼和浩特 010022
    基金项目: 国家自然科学基金(批准号: 10862003)、内蒙古自治区高等学校科学研究基金 (批准号: NJZY12031)和 内蒙古自治区自然科学基金(批准号: 2010MS0111)资助的课题.

摘要: 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.

English Abstract

参考文献 (57)

目录

    /

    返回文章
    返回