一类非线性发展方程的复合型双孤子新解

套格图桑; 伊丽娜

doi:10.7498/aps.64.020201

摘要

通过下列步骤,构造了一类非线性发展方程的无穷序列复合型双孤子新解: 步骤一, 给出两种函数变换,把一类非线性发展方程化为二阶非线性常微分方程; 步骤二, 再通过函数变换, 二阶非线性常微分方程转化为一阶非线性常微分方程组,并获得了该方程组的首次积分; 步骤三, 利用首次积分与两种椭圆方程的新解与Bäcklund 变换, 构造了一类非线性发展方程的无穷序列复合型双孤子新解.

关键词:

New infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation are constructed with the help of function transformations and two kinds of elliptic equations. Step one，according to two function transformations, a kind of nonlinear evolution equation is changed into a nonlinear ordinary differential equation of second order. Step two, using function transformation, the nonlinear ordinary differential equation of second order is transformed into a set of nonlinear ordinary differential equations of first order, and the first integral of the set of equations is obtained. Finally, the first integral with new solutions and Bäcklund transformation of two kinds of elliptic equations are used to search for new infinite sequence complexion two-soliton solutions of a kind of nonlinear evolution equation.

Keywords:

作者及机构信息

1.
内蒙古师范大学, 数学科学学院, 呼和浩特 010022

基金项目: 国家自然科学基金资助项目(批准号: 11361040)和内蒙古自治区高等学校科学研究基金(批准号: NJZY12031)资助的课题.

Authors and contacts

1.
The College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11361040) and the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region, China (Grant No. NJZY12031).

参考文献

[1]	Schäfer T, Wayne C E 2004 Physica D 196 90
[2]	Pietrzyk M, Kanattsšikov I, Bandelow U 2008 J. Nonli- near Math. Phys. 15 162
[3]	Sakovich S 2008 J. Phys. Soc. Jpn. 77 123001
[4]	Rui W G 2013 Commun. Nonlinear. Sci. Numer. Simulat. 18 2678
[5]	Sun W R, Tian B, Jiang Y, Zhen H L 2014 Annals. Phys. 343 215
[6]	Wang Y F, Tian B, Li M, Wang P, Wang M 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 1783
[7]	Zuo D W, Gao Y T, Meng G Q, Shen Y J, Yu X 2014 Nonlinear Dyn. 75 701
[8]	Sun Z Y, Gao Y T, Yu X, Liu Y 2013 Phys. Lett. A 377 3283
[9]	Taogetusang, Bai Y M 2012 Acta Phys. Sin. 61 060201 (in Chinese) [套格图桑, 白玉梅 2012 物理学报 61 060201]
[10]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. 55 949
[11]	Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. 19 080303
[12]	Taogetusang 2011 Acta Phys. Sin. 60 050201 (in Chinese) [套格图桑 2011 物理学报 60 050201]
[13]	Wang J M 2012 Acta Phys. Sin. 61 080201 (in Chinese) [王军民 2012 物理学报 61 080201]
[14]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[15]	Li Z L 2009 Chin. Phys. B 18 4074
[16]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 39 135
[17]	Zhang L, Zhang L F, Li C Y 2008 Chin. Phys. B 17 403
[18]	Xie F D, Gao X S 2004 Commun. Theor. Phys. 41 353
[19]	Taogetusang, Sirendaoerji 2006 Chin. Phys. 15 1143
[20]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. 40 143
[21]	Xu G Q, Li Z B 2003 Commun. Theor. Phys. 39 39
[22]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417

施引文献

[1]	Schäfer T, Wayne C E 2004 Physica D 196 90
[2]	Pietrzyk M, Kanattsšikov I, Bandelow U 2008 J. Nonli- near Math. Phys. 15 162
[3]	Sakovich S 2008 J. Phys. Soc. Jpn. 77 123001
[4]	Rui W G 2013 Commun. Nonlinear. Sci. Numer. Simulat. 18 2678
[5]	Sun W R, Tian B, Jiang Y, Zhen H L 2014 Annals. Phys. 343 215
[6]	Wang Y F, Tian B, Li M, Wang P, Wang M 2014 Commun. Nonlinear Sci. Numer. Simulat. 19 1783
[7]	Zuo D W, Gao Y T, Meng G Q, Shen Y J, Yu X 2014 Nonlinear Dyn. 75 701
[8]	Sun Z Y, Gao Y T, Yu X, Liu Y 2013 Phys. Lett. A 377 3283
[9]	Taogetusang, Bai Y M 2012 Acta Phys. Sin. 61 060201 (in Chinese) [套格图桑, 白玉梅 2012 物理学报 61 060201]
[10]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. 55 949
[11]	Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. 19 080303
[12]	Taogetusang 2011 Acta Phys. Sin. 60 050201 (in Chinese) [套格图桑 2011 物理学报 60 050201]
[13]	Wang J M 2012 Acta Phys. Sin. 61 080201 (in Chinese) [王军民 2012 物理学报 61 080201]
[14]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[15]	Li Z L 2009 Chin. Phys. B 18 4074
[16]	Chen Y, Li B, Zhang H Q 2003 Commun. Theor. Phys. 39 135
[17]	Zhang L, Zhang L F, Li C Y 2008 Chin. Phys. B 17 403
[18]	Xie F D, Gao X S 2004 Commun. Theor. Phys. 41 353
[19]	Taogetusang, Sirendaoerji 2006 Chin. Phys. 15 1143
[20]	Li D S, Zhang H Q 2003 Commun. Theor. Phys. 40 143
[21]	Xu G Q, Li Z B 2003 Commun. Theor. Phys. 39 39
[22]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417

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