Nizhnik-Novikov-Vesselov方程的无穷序列类孤子精确解

套格图桑; 白玉梅

doi:10.7498/aps.61.110203

摘要

为了构造非线性发展方程的无穷序列类孤子精确解, 发掘第一种椭圆辅助方程的构造性和机械化性特点, 获得了该方程的一些新类型解和相应的 Bcklund变换. 在此基础上利用符号计算系统Mathematica构造了Nizhnik-Novikov-Vesselov方程的无穷序列类孤子精确解, 包括无穷序列光滑类孤子解、无穷序列类尖峰孤立子解和无穷序列类紧孤立子解.

关键词:

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.

Keywords:

作者及机构信息

套格图桑^1,2,
白玉梅²

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.

Authors and contacts

Taogetusang^1,2,
Bai Yu-Mei²

1.
College of Mathematical, Inner Mongolia University for Nationalities, Tongliao 028043, China;

2.
College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Funds: Project supported by the National 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).

参考文献

[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]

施引文献

[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]

[1]	套格图桑, 伊丽娜. sine-Gordon型方程的无穷序列新解. , 2014, 63(21): 210202. doi: 10.7498/aps.63.210202
[2]	套格图桑, 伊丽娜. Camassa-Holm-r方程的无穷序列类孤子新解. , 2014, 63(12): 120201. doi: 10.7498/aps.63.120201
[3]	套格图桑. (2+1)维广义Calogero-Bogoyavlenskii-Schiff方程的无穷序列类孤子解. , 2013, 62(21): 210201. doi: 10.7498/aps.62.210201
[4]	徐兰兰, 陈怀堂. 变系数(2+1)维Nizhnik-Novikov-Vesselov方程的三孤子新解. , 2013, 62(9): 090204. doi: 10.7498/aps.62.090204
[5]	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. , 2012, 61(13): 130202. doi: 10.7498/aps.61.130202
[6]	白玉梅, 套格图桑, 韩元春. K(m,n)方程与B(m,n)方程的无穷序列新精确解. , 2012, 61(20): 200205. doi: 10.7498/aps.61.200205
[7]	套格图桑, 白玉梅. 第二类变系数KdV方程的新类型无穷序列精确解. , 2012, 61(6): 060201. doi: 10.7498/aps.61.060201
[8]	套格图桑. Degasperis-Procesi 方程的无穷序列尖峰孤立波解. , 2011, 60(7): 070204. doi: 10.7498/aps.60.070204
[9]	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. , 2011, 60(9): 090201. doi: 10.7498/aps.60.090201
[10]	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. , 2011, 60(5): 050201. doi: 10.7498/aps.60.050201
[11]	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. , 2011, 60(1): 010202. doi: 10.7498/aps.60.010202
[12]	套格图桑. sine-Gordon型方程的无穷序列新精确解. , 2011, 60(7): 070203. doi: 10.7498/aps.60.070203
[13]	套格图桑, 斯仁道尔吉. 广义Boussinesq方程的无穷序列新精确解. , 2010, 59(7): 4413-4419. doi: 10.7498/aps.59.4413
[14]	套格图桑. 一般格子方程新的无穷序列精确解. , 2010, 59(10): 6712-6718. doi: 10.7498/aps.59.6712
[15]	套格图桑, 斯仁道尔吉. 构造变系数非线性发展方程精确解的一种方法. , 2009, 58(4): 2121-2126. doi: 10.7498/aps.58.2121
[16]	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. , 2006, 55(12): 6214-6221. doi: 10.7498/aps.55.6214
[17]	李德生, 张鸿庆. 非线性演化方程椭圆函数解的一种简单求法及其应用. , 2006, 55(4): 1565-1570. doi: 10.7498/aps.55.1565
[18]	曾昕, 张鸿庆. (2+1)维Boussinesq方程的Backlund变换与精确解. , 2005, 54(4): 1476-1480. doi: 10.7498/aps.54.1476
[19]	阮航宇, 陈一新. 2+1维Nizhnik-Novikov-Veselov方程中孤子相互作用的探索. , 2003, 52(6): 1313-1318. doi: 10.7498/aps.52.1313
[20]	李画眉. (3+1)维Nizhnik-Novikov-Veselov方程的孤子解和周期解. , 2002, 51(3): 465-467. doi: 10.7498/aps.51.465

计量

文章访问数: 7353
PDF下载量: 737
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板