sine-Gordon型方程的无穷序列新解

套格图桑; 伊丽娜

doi:10.7498/aps.63.210202

摘要

通过下列步骤,获得了sine-Gordon型方程的新解.第一步、通过函数变换,把sine-Gordon方程与sinh-Gordon方程的求解问题转化为两种非线性常微分方程的求解问题. 第二步、获得了两种非线性常微分方程与第一种椭圆方程的拟Bcklund变换.第三步、利用第一种椭圆方程的Bcklund 变换与新解,构造了sine-Gordon 型方程的无穷序列新解.

关键词:

The following steps are given to search for new solutions to equations of sine-Gordon type. Step one, according to function transformation, the solving of sine-Gordon equation and sinh-Gordon equation is changed into the solving of two kinds of nonlinear ordinary differential equations. Step two, two kinds of nonlinear ordinary differential equations and quasi-Bcklund transformation of the first kind of elliptic equation are obtained. Finally, new infinite sequence solutions to equations of sine-Gordon type are constructed by applying Bcklund transformation and new solutions of the first kind of elliptic 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(批准号:11361040)、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

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), 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]	Sirendaoerji, Sun J 2002 Phys. Lett. A 298 133
[2]	Xie Y X, Tang J S 2005 Chin. Phys. 14 1303
[3]	Liu C S 2008 Commun. Theor. Phys. 49 153
[4]	Xu Z H, Chen H L, Xian D Q 2012 Commun. Theor. Phys. 57 400
[5]	Taogetusang, Bai Y M 2013 Acta Phys. Sin. 62 100201 (in Chinese) [套格图桑, 白玉梅 2013 物理学报 62 100201]
[6]	Sirendaoreji, Sun J 2003 Phys. Lett. A 309 387
[7]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[8]	L Z S, Zhang H Q 2003 Commun. Theor. Phys. 39 405
[9]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[10]	Ma S H, Fang J P 2012 Acta Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 物理学报 61 180505]
[11]	Liu S K, Fu Z T, Liu S D 2002 Acta Phys. Sin. 51 1923 (in Chinese) [刘式适, 付遵涛, 刘式达 2002 物理学报 51 1923]
[12]	Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[13]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417
[14]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. 55 949
[15]	Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303

施引文献

[1]	Sirendaoerji, Sun J 2002 Phys. Lett. A 298 133
[2]	Xie Y X, Tang J S 2005 Chin. Phys. 14 1303
[3]	Liu C S 2008 Commun. Theor. Phys. 49 153
[4]	Xu Z H, Chen H L, Xian D Q 2012 Commun. Theor. Phys. 57 400
[5]	Taogetusang, Bai Y M 2013 Acta Phys. Sin. 62 100201 (in Chinese) [套格图桑, 白玉梅 2013 物理学报 62 100201]
[6]	Sirendaoreji, Sun J 2003 Phys. Lett. A 309 387
[7]	Chen Y, Li B, Zhang H Q 2003 Chin. Phys. 12 940
[8]	L Z S, Zhang H Q 2003 Commun. Theor. Phys. 39 405
[9]	Li D S, Zhang H Q 2004 Chin. Phys. 13 984
[10]	Ma S H, Fang J P 2012 Acta Phys. Sin. 61 180505 (in Chinese) [马松华, 方建平 2012 物理学报 61 180505]
[11]	Liu S K, Fu Z T, Liu S D 2002 Acta Phys. Sin. 51 1923 (in Chinese) [刘式适, 付遵涛, 刘式达 2002 物理学报 51 1923]
[12]	Lu D C, Hong B J, Tian L X 2006 Acta Phys. Sin. 55 5617 (in Chinese) [卢殿臣, 洪宝剑, 田立新 2006 物理学报 55 5617]
[13]	Wang M L, Li X Z, Zhang J L 2008 Phys. Lett. A 372 417
[14]	Taogetusang, Sirendaoerji, Li S M 2011 Commun. Theor. Phys. 55 949
[15]	Taogetusang, Sirendaoerji, Li S M 2010 Chin. Phys. B 19 080303

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