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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.
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关键词:
- 函数变换 /
- sine-Gordon型方程 /
- 第一种椭圆方程 /
- 无穷序列新解
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:
- function transformation /
- equations of sine-Gordon type /
- the first kind of elliptic equation /
- new infinite sequence solutions
[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 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 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 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 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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[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 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 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 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 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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